Yuzhou Fang, Chao Zhang
We consider interior Hölder regularity of the spatial gradient of viscosity solutions to the normalized $p(x,t)$-Laplace equation $$ u_t=\left(δ_{ij}+(p(x,t)-2)\frac{u_i u_j}{|Du|^2}\right)u_{ij} $$ with some suitable assumptions on $p(x,t)$, which arises naturally from a two-player zero-sum stochastic differential game with probabilities depending on space and time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Optimal in tail Hölder estimates for weak solutions of the nonlocal parabolic p-Laplace equations on the Heisenberg group
本文研究了海森堡群上非局部抛物p-拉普拉斯方程弱解的最优尾Hölder估计问题，通过引入最优尾条件证明了弱解的Hölder连续性。
We study Hölder continuity for solutions of the $p$-Laplace equation. This is established through a method involving an ordinary differential inequality, in contrast to the classical proof of the De Giorgi-Nash-Moser Theorem which uses iteration of an inequality through concentric balls.
We give a unified proof of Hölder regularity of weak solutions for mixed local and nonlocal $p$-Laplace type parabolic equations with the full range of exponents $1<p<\infty$. Our proof is based on the expansion of positivity together with the energy estimate and De Giorgi type lemma.
We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized $p(x)$-Laplace equation $$ -Δu-(p(x)-2)\frac{\left\langle D^{2}uDu,Du\right\rangle }{\left|Du\right|^{2}} = f(x), $$ where $p$ is Lipschitz continuous, $\inf p>1$, and $f$ is continuous and bounded.
We show that bounded solutions of the quasilinear elliptic equation $Δ_{p(x)} u=g+div(\textbf{F})$ are locally Hölder continuous provided that the functions $g$ and $\textbf{F}$ are in suitable Lebesgue spaces.
In this note, we prove the boundary Hölder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exterior cone condition, the Reifenberg flat domains, and the corkscrew domains (including the non-tangentially accessible domains) are special cases. The key idea, following [3], is that the strong maximum principle and the scaling invariance imply the boundary Hölder regularity.
We study parabolic equations in variable Hölder spaces on domains of Euclidean spaces. The existence and uniqueness of solutions is proved.
In this paper, we obtain local Hölder regularity for bounded, weak solutions to the anisotropic $p$-Laplace equation whose prototype structure is given by $$ \sum_{i=1}^N (|u_{x_i}|^{p_i-2}u_{x_i})_{x_i}=0,$$ where $1 < p_1 \leq p_2 \leq \cdots \leq p_N < \infty$. Under an additional assumption that double truncates of the solution are sub/super solution, we obtain Hölder regularity for the anisotropic equation.
On $(p,q)$-eigenvalues of the weighted $p$-Laplace operator in outward Hölder cuspidal domains
本文研究向外Hölder尖角域中加权$p$-Laplace算子的Neumann $(p,q)$-特征值问题，方法基于加权Sobolev空间上的复合算子。
We give an alternative proof for Hölder regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by a continuous iteration. This work can be viewed as the nonlocal counterpart to the ideas developed by Tiziano Granucci.
We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with Hölder continuous coefficients. The result we obtain is essentially based on parametrix method.
This paper proves Hölder continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first shows that viscosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative are Hölder continuous.
We give a proof for the Hölder continuity of functions in the parabolic De Giorgi classes in metric measure spaces. We assume the measure to be doubling, to support a weak $(1,p)$-Poincaré inequality and to satisfy the annular decay property.
Quantitative uniqueness for parabolic equations with Hölder potentials
本文研究了具有Hölder零阶项的抛物算子的空间-like定量化唯一性，扩展了Teng等人关于时间不变Schrödinger算子的研究。
We study local boundedness and Hölder continuity of a parabolic equation involving the fractional $p$-Laplacian of order $s$, with $0<s<1$, $2\leq p < \infty$, with a general right hand side. We focus on obtaining precise Hölder continuity estimates. The proof is based on a perturbative argument using the already known Hölder continuity estimate for solutions to the equation with zero right hand side.
Motivated by an equation arising in magnetohydrodynamics, we prove that Holder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner, combined with energy estimates, without any minimality assumption on the Holder exponent of the weak solutions.
Boundary Hölder gradient estimates for parabolic $p$-Laplace type equations
本文研究了抛物 $p$-Laplace 型方程粘性解的边界正则性，获得了边界逐点和全局 $C^{1,α}$ 正则性。
We prove Hölder estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV} \int_{\mathbb{R}^n}\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\, dy =0, $$ where $s\in (0,1)$ and $p>2$ or $1/(1-s)<p<2$. Our results also apply for inhomogeneous equations with more general kernels, when $p$ and $s$ are allowed to vary with $x$, without any regularity assumption on $p$ and $s$. This complements and extends some of the recently obtained Hölder estimates for weak solutions.
We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.
Higher Hölder regularity for nonlocal parabolic equations with irregular kernels
本文研究了具有不规则核系数的非局部抛物型方程，在对非齐次项施加适当高阶可积性且对核系数作最小正则性假设的条件下，建立了该方程的高阶Hölder正则性。
In this paper we prove a Hölder propagation of smallness for solutions to second order parabolic equations whose general anisotropic leading coefficient has a jump at an interface. We assume that the leading coefficient is Lipschitz continuous with respect to the parabolic distance on both sides of the interface. The main effort consists in proving a local Carleman estimate for this parabolic operator.
We investigate existence and regularity of weak solutions of a 1-dimensional parabolic differential equation with a non-constant Hölder diffusion coefficient and a rough forcing term. Such an equation appears in studying the 1-dimensional Ericksen-Leslie model for nematic liquid crystals where our result applies. The result presented here uses the Hölder continuity of the diffusion coefficient which comes from the physical background and the analysis of the Ericksen-Leslie model. Moreover, the dependence of the Hölder exponent of the solution is explicit on the Hölder exponent of the diffusion…
Global Hölder Solvability of parabolic equations on domains with capacity density conditions
本文研究了具有容量密度条件的领域上抛物型方程的全局Hölder解的存在性，允许数据在边界附近具有临界奇异性。
Hölder regularity for degenerate parabolic double-phase equations
本文证明了p-Laplace型退化抛物双相方程的有界弱解具有局部Hölder连续性，其核心方法是通过相位分析判断方程局部类似于p-Laplace还是q-Laplace方程。
We prove interior Hölder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous $p$-Laplacian equation \[ u_t=|\nabla u|^{2-p} \mbox{ div} (|\nabla u|^{p-2}\nabla u), \] where $1<p<\infty$. This equation arises from tug-of-war-like stochastic games with noise. It can also be considered as the parabolic $p$-Laplacian equation in non divergence form.
We investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness and ellipticity on the coefficient function and very mild conditions on the geometry of the domain, including a very weak compatibility condition between the Dirichlet boundary part and its complement, we prove Hölder continuity of the solution in space and time.
Higher Hölder regularity for fractional $(p,q)$-Laplace equations
本文研究分数阶 $(p,q)$-Laplace 方程，建立了具有显式指数的 Hölder 估计，并推导出 Liouville 型定理，方法基于差商的 Moser 型迭代。
We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling non-trivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.
We establish the local Hölder continuity for the nonnegative weak solutions of certain doubly nonlinear parabolic equations possessing a singularity in the time derivative part and a degeneracy in the principal part. The proof involves the method of intrinsic scaling and the setting is a measure space equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality.
Local Hölder regularity is established for certain weak solutions to a class of parabolic fractional $p$-Laplace equations with merely measurable kernels. The proof uses DeGiorgi's iteration and refines DiBenedetto's intrinsic scaling method. The control of a nonlocal integral of solutions in the reduction of oscillation plays a crucial role and entails delicate analysis in this intrinsic scaling scenario. Dispensing with any logarithmic estimate and any comparison principle, the proof is new even for the linear case.
Higher Hölder regularity for the fractional $p$-Laplace equation in the subquadratic case
本文研究了次二次情形下分数阶 $p$-Laplace 方程，通过 Moser 型迭代与扰动论证，给出了具有显式指数的 Hölder 估计，并补充了超二次情形的已有结果。
In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non necessarily symmetric which could be interpreted as a non-local drift with the same order as the diffusion. We provide an Oscillation Lemma and a Harnack Inequality which can be used to prove higher regularity estimates.
This paper deals with two separate but related results. First we consider weak solutions to a parabolic operator with Hörmander vector fields. Adapting the iteration scheme of Jürgen Moser for elliptic and parabolic equations in $\mathbb{R}^n$ we show a parabolic Harnack inequality. Then, after proving the Harnack inequality for weak solutions to equations of the form $u_t = \sum X_i (a_{ij} X_j u)$ we use this to show Hölder continuity. We assume the coefficients are bounded and elliptic. The iteration scheme is a tool that may be adapted to many settings and we extend this to nonlinear parab…
In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity. Our investigation reveals that weak solutions are Hölder continuous when the space dimension $N$ is $2$. This is achieved via an inequality associated with the Stummel-Kato class of functions and refinement of a lemma originally due to S. Campanato and C. B. Morrey (\cite{G}, p. 86).
Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations
本文针对完全非线性退化或奇异抛物型方程，利用紧性方法、障碍函数构造、正则化技术及小扰动解的边界正则性，建立了统一的边界Hölder梯度估计，推广了已有结果。
Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities
该研究证明了带至多线性增长Hölder连续非线性项的半线性抛物演化方程对广泛初值存在全局强解，并将结果应用于丛林火灾波前传播模型与反应扩散系统。
We prove interior Hölder estimate for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation $$ u_t=|\nabla u|^κ\mbox{div} (|\nabla u|^{p-2}\nabla u), $$ where $p\in (1,\infty)$ and $κ\in (1-p,\infty).$ This includes the from $L^\infty$ to $C^{1,α}$ regularity for parabolic $p$-Laplacian equations in both divergence form with $κ=0$, and non-divergence form with $κ=2-p$. This work is a continuation of a paper by the last two authors \cite{JS}.
The parabolic normalized p-Laplace equation is studied. We prove that a viscosity solution has a time derivative in the sense of Sobolev belonging locally to $L^2$.
The Hölder interpolative gap bound for degenerate parabolic double phase problems
针对退化抛物双相方程，在解具有Hölder连续性时，提出并证明了满足间隙条件$q\le p+\alpha/(1-\gamma)$的梯度更高可积性，首次给出Hölder插值型间隙界。
In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the Hölder regularity for bounded solutions to parabolic-parabolic as well as for elliptic-parabolic chemotaxis systems.
Hölder Continuity for Fully Fractional Parabolic Equations with Space-time Nonlocal Operators
本文研究含空间分数阶扩散与Marchaud型分数阶时间导数的全分数阶抛物型方程，在不假设解和非齐次项有界的条件下，引入时间依赖非局部尾项，利用非局部De Giorgi迭代技术证明弱解的局部有界性与局部Hölder连续性。
Higher order parabolic systems with piecewise DMO and Hölder continuous coefficients
本文研究了柱状域内含有限子域的散度型高阶抛物系统，在主系数与非齐次项分别满足分段 Dini 平均振荡与分段 Hölder 连续性的条件下，建立了该系统解的 $L_\infty$ 与 Schauder 估计，填补了高阶椭圆与抛物系统该类研究的空白。
In this paper we establish optimal solvability results, that is, maximal regularity theorems, for the Cauchy problem for linear parabolic differential equations of arbitrary order acting on sections of tensor bundles over boundaryless complete Riemannian manifolds with bounded geometry. We employ an anisotropic extension of the Fourier multiplier theorem for arbitrary Besov spaces introduced in earlier by the author. This allows for a unified treatment of Sobolev-Slobodeckii and little Hölder spaces. In the flat case we recover classical results for Petrowskii-parabolic Cauchy problems.
We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the case $p\geq 2$ that if the right hand side $g$ is locally in $L^\infty(\text{BMO})$, then $u$ is locally in $L^\infty(\mathcal{C}^1)$, where $\mathcal{C}^1$ is the 1-Hölder--Zygmund space. This is the borderline case of the Calderón-Zygmund theorey. We provide local quantitative estimates. We also show that finer properties of $g$ are conserved by $D u$, e.g.\ Hölder continuity. Moreover, we prove a new decay for gradients of $p$-caloric solut…
Interpolated time-Hölder regularity of solutions of fully nonlinear parabolic equations
本文通过最大原理，为特定类型的完全非线性抛物Isaacs方程建立了内部Schauder估计，并证明了模型方程的Evans-Krylov结果，同时为具有平稳非齐次方程正则性理论的完全非线性均匀抛物方程证明了Evans-Krylov定理。
The present paper is devoted to studying of some weighted Hölder spaces. These spaces are designed in the way to serve as a framework for studying different statements for the thin film equations in weighted classes of smooth functions in the multidimensional setting. These spaces can serve also for considering of other equations with the degeneration on the boundary of the domain of definition.
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate
本文针对抛物型 MEMS 方程的淬灭现象，运用爆破方法与 Liouville 定理建立解的最优 Hölder 估计及一致连续解序列的收敛理论，并据此证明破裂集分层定理。
We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments for the normalized p-parabolic operator, we show that the gradient of bounded viscosity solutions is locally asymptotically Lipschitz continuous when $p$ is sufficiently close to 2. In addition, we establish regularity estimates in Sobolev spaces.
Hölder Continuity and Harnack estimate for non-homogeneous parabolic equations
本文针对非散度型非齐次抛物型方程，建立了时间向前的内在Harnack不等式，由此导出解的Hölder连续性，并给出量化强最小值原理的全局Harnack型估计，为广义Harnack不等式提供了新证明。
In this paper, we study the second order Sobolev regularity of solutions to the parabolic $p$-Laplace equation. For any $p$-parabolic function $u$, we show that $D(|Du|^{\frac{p-2+s}{2}}Du)$ exists as a function and belongs to $L^{2}_{\text{loc}}$ with $s>-1$ and $1<p<\infty$. The range of $s$ is sharp.
In this paper we study an evolution equation involving the normalized $p$-Laplacian and a bounded continuous source term. The normalized $p$-Laplacian is in non divergence form and arises for example from stochastic tug-of-war games with noise. We prove local $C^{α, \fracα{2}}$ regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p- Laplace parabolic equations on the Heisenberg group, and characterize the viscosity solutions in terms of an asymptotic mean value formula. Moreover, we construct an example to show that these formulae do not hold in non-asymptotic sense.
Higher Hölder regularity for a subquadratic nonlocal parabolic equation
本文研究含分数阶$p$-Laplacian（$0<s<1$，$1<p<2$）的次二次非局部抛物方程解的Hölder正则性，建立了具显式且几乎最优指数的正则性结果，并涵盖有界非齐次项情形，补充了$p\geq 2$超二次情形的已有研究。
We investigate the mixed local and nonlocal parabolic $p$-Laplace equation \begin{align*} \partial_t u(x,t)-Δ_p u(x,t)+\mathcal{L}u(x,t)=0, \end{align*} where $Δ_p$ is the local $p$-Laplace operator and $\mathcal{L}$ is the nonlocal $p$-Laplace operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi-Nash-Moser iteration, we establish the local boundedness and Hölder continuity of weak solutions for such equations.
Weak parabolic Harnack inequality and Hölder regularity for non-local Dirichlet forms
本文研究一般正则狄利克雷型，通过局部热核估计与增长引理建立弱抛物型哈纳克不等式的等价条件，并在取消上跳跃光滑性假设的情形下证明热函数与调和函数的赫尔德连续性，推广了已有理论。
We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional $p$-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi's method. Furthermore, by means of a new algebraic inequality, we show that positive weak supersolutions satisfy a reverse Hölder inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.
James Serrin's fundamental contributions to the theory of quasilinear elliptic equations are well-known and widely appreciated. He also made less well-known contributions to the theory of quasilinear parabolic equations which we dicuss in this note. Jurgen Moser gave greatly simplified proofs of the De Giorgi-Nash regularity results for linear divergence structure elliptic and parabolic differential equations using an original iterative technique. Serrin extended Moser's techniques and applied them to the study of divergence structure quasilinear elliptic equations, and in collaboration with A…
We consider a Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces. The equation generalizes the heat equation to the case of fractional power of the Laplace operator and the power of this operator can be different with respect to different groups of space variables. The time derivative can be either fractional Caputo - Jrbashyan derivative or usual derivative. Under some necessary conditions on the order of the time derivative we show that the operator of the whole problem is an isomorphism of appropriate anisotropic Hölder spaces. Under some another con…
Local Hölder regularity for nonlocal parabolic $p$-Laplace equations
本文针对一类非局部抛物型 $p$-Laplace 方程，在 $p\in (1,\infty)$ 且 $s \in (0,1)$ 的条件下，证明了其解具有局部 Hölder 正则性。
Hölder regularity for the parabolic perturbed fractional 1-Laplace equations
本文研究了一类抛物型扰动分数1-拉普拉斯方程弱解的正则性，结合差分商、能量估计和迭代方法，通过分解非局部积分处理其贡献，证明弱解在抛物域内局部Hölder连续，建立Sobolev正则性以推导Hölder连续性。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。