An Interior Estimate for a Nonlinear Parabolic Equation
Giuseppe Maria Coclite
本文利用边界值的全变差和初始条件的L^{infinity}-范数，估计了一类非线性一致抛物型方程初边值问题解的导数.
In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of the initial condition.
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
Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations
给出了非光滑系数在内点退化的抛物型方程的Carleman估计、能观性不等式和零能控性结果。
Characterizations of interior polar sets for the degenerate p-parabolic equation
本文讨论了非线性抛物型p-Laplace方程的容量零点集的不同刻画。具体地说，我们证明了某些内部极集可以由零非线性抛物容量集的特点。此外，我们证明了零容量集是可移动的有界上解和零容量集有一定的抛物型Hausdorff措施的关系。
Time-interior gradient estimates for quasilinear parabolic equations
各种各样的拟线性抛物型方程的Dirichlet和Neumann问题的有界光滑解，包括图形各向异性的中曲率流，在振荡和时间上都有梯度界.
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of such solutions after gradient blow-up. This continuation is global in time and we give an example when it never becomes a classical solution again.
Carleman estimates for singular parabolic equations with interior degeneracy and non smooth coefficients
我们建立了奇异/退化抛物狄利克雷问题的Carleman估计，退化和奇异性发生在空间域的内部。我们的结果是全新的，因为这种情况是不包括以前的贡献退化和奇异的边界。此外，我们考虑非光滑系数，从而防止在这个框架中使用标准计算。
Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates
考虑具有Dirichlet或Neumann边界条件的非散度型退化奇异非光滑一般抛物型方程.特别是，我们认为适定性的问题，然后我们证明了Carleman估计相关的伴随问题。
Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions
本文考虑了一个在空间域内部具有退化项和Neumann边界条件的抛物问题。特别是，我们将专注于适定性的问题和Carleman估计相关的伴随问题。本论文的新颖之处在于，第一次被认为是一个内部退化和Neumann边界条件的问题，使以前的结果可以适应这种情况。因此，建立了新的可观性不等式。
Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets
本文利用紧性方法与扰动技术证明散度型椭圆和抛物方程弱解的最优内部逐点 $C^{k,\alpha}$ 正则性，并将其用于刻画解的节点集结构。
Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts
本文针对带无散漂移项的椭圆与抛物方程，利用能量不等式和扰动技术，在三类小漂移条件下证明弱解对任意 $0<α<1$ 的内部逐点 $C^α$ 正则性。
In this paper, we establish the gradient and Pogorelov estimates for $k$-convex-monotone solutions to parabolic $k$-Hessian equations of the form $-u_tσ_k(λ(D^2u))=ψ(x,t,u)$. We also apply such estimates to obtain a Liouville type result, which states that any $k$-convex-monotone and $C^{4,2}$ solution $u$ to $-u_tσ_k(λ(D^2u))=1$ in $\mathbb{R}^n\times(-\infty,0]$ must be a linear function of $t$ plus a quadratic polynomial of $x$, under some growth assumptions on $u$.
Interior Calderón-Zygmund estimates for solutions to general parabolic equations of $p$-Laplacian type
我们研究一般的抛物型方程的形式$u_t = div A(x,t, u,D u) + div(|F|^{p-2} F)+ f$的主要部分取决于解决方案本身。假设矢量场$A$在$x$中具有小的平均振荡，在$t$中可测量，在$u$中Lipschitz连续，并且其在$Du$中的增长类似于$p$ -拉普拉斯算子。当满足$p>2n/(n+2)$时，我们建立了方程局部有界弱解的内部Calderón-Zygmund估计.这是通过采用扰动方法与开发一个双参数技术和一个新的紧凑性参数。我们还利用DiBenedetto \cite{D2}的内在几何方法和Acerbi和Mingione \cite{AM}的极大函数自由方法。
Interior Lp-estimates for elliptic and parabolic Schrödinger type operators and local Ap-weights
设Ω是R^n的非空开真连通子集。考虑Ω中p椭圆薛定谔型算子L_{E} u= A_{E} u+V和Ω x（0，T）中线性抛物算子L_{P} u= A_{P} u+Vu，其中A_{E}和A_{P}的系数都在VMO中，势V满足逆赫尔德条件.本文的目的是获得算子L_{E}和L_{P}在加权索伯列夫空间中的先验估计，其中涉及到边界的距离和局部A类的权.
Interior Sobolev regularity for fully nonlinear parabolic equations
在本文中，我们建立了完全非线性抛物型方程解的精确Sobolev估计，在极小的，渐近的，对控制算子的假设。特别是，我们证明了解决方案是在$W^{2,1;p}_{loc}$。我们的论点展开进口改进的规律性从一个限制配置。在这种具体情况下，我们求助于与$F$相关的衰退函数。这种机制允许我们在$\mathcal{S}(d)$的无穷远处仅对原始算子施加条件。从启发式的观点来看，积分正则性将由该空间两端的$F$的行为来设置。此外，我们探讨了一些后果，我们的研究结果，并制定了一些相关的结果，其中包括一个抛物线版本的Escauriaza的指数，一个通用的模数连续性的解决方案和估计$p-BMO$空间。
Interior regularity of mixed local-nonlocal parabolic semilinear equations
本文证明混合局部-非局部扩散算子半线性抛物方程经典解的存在唯一性，并建立其空间与时间 Hölder 连续性及空间 $C^{2,\alpha}_{loc}$ 内部正则性。
Carleman estimates and observability inequalities for parabolic equations with interior degeneracy
我们考虑一个抛物型问题的退化的空间域的内部，我们专注于可控性的结果，通过Carleman估计相关的伴随问题。本文的新颖之处在于，退化也是在内部的控制区域，使以前的结果可以适应这种情况。
This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior $C^{1, α}$ and $C^{2, α}$ estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.
We obtain parabolic transmission eigenvalue-free regions for both isotropic andanisotropic interior transmission problems with coefficients which are Lipschitznear the boundary
Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy
研究了一类强退化抛物型扩散方程的两个识别问题，其特征在于扩散系数$u\in W^{1,\infty},$为零，性质为$\frac{1}{u}\notin L^{1}. $.目的是利用系数控制的非线性最优控制技术，从解的某些观测值中识别出$u$.对于齐次Dirichlet边界条件，给出了在$% W^{1,\infty}$中搜索的控制器$u$的存在性和最优性条件的确定.进一步引入的近似问题，允许更好地表征的最优性条件，由于补充的正则性的近似状态和对偶函数和收敛结果。最后，考虑了状态系统中具有末次观测和齐次Dirichlet-Neumann边界条件的辨识问题。通过使用更多的技术论证，我们给出了$u$的显式形式及其唯一性.
$C^{1,\al}$ regularity of solutions to parabolic Monge-Ampére equations
研究了抛物型Monge-Ampére方程$$u_t = b(x,t) \ddua,$$黏性解的内部$C^{1, \al}$正则性，其中指数为$p >0$，系数为有界可测的$b$.我们表明，当$p$小于临界功率$\frac{1}{n-2}$，然后解决方案立即成为$C^{1, \al}$在内部。此外，我们证明了相同的结果，任何电源$p>0$在这些点上，无论是从初始数据的解决方案分离，或在初始数据是$C^{1, β}$。
Solvability of interior transmission problem for the diffusion equation by constructing its Green function
考虑具有间断扩散系数的扩散方程反边值问题的内传递问题。通过构造内传播问题的格林函数，证明了内传播问题的唯一可解性。首先，我们利用大参数伪微分算子理论，在Laplace域中构造了一个局部参数方程，用于求解边界附近的内部传输问题。其次，通过分析Laplace域内局部参数的解析性，并在Laplace域内对其进行估计，利用拉普拉斯逆变换得到了原抛物型内传播问题的局部参数。最后，利用单位分解，对所有局部参数和扩散方程的基本解进行修补，生成抛物型内传输问题的全局参数，然后对全局参数进行补偿，得到格林函数。利用对偶性证明了格林函数的唯一性，从而得出了内传递问题的唯一可解性。本文首次构造了抛物型内透射问题的格林函数。该方法可应用于主动热成像和扩散方程模型的扩散光学层析成像，以识别未知夹杂物及其物理性质。
Interior derivative estimates and Bernstein theorem for Hessian quotient equations
本文针对椭圆型和抛物型Hessian商方程建立了内部导数估计，并在此基础上证明了抛物型Hessian商方程的Bernstein定理，刻画了全局抛物凸解必为线性时间项与凸二次多项式之和的形式。
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces
在松弛的凸性条件下，证明了全空间中完全非线性椭圆型和抛物型方程的加权和混合范数Sobolev估计，其中几乎VMO依赖于时空变量.得到了相应的内点估计和边界估计。
Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue Spaces
本文研究了在某个区域$Q\subset \mathbb{R}^{n+1}$上具有漂移\[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\]的二阶非散度型一致抛物型方程和不等式.主要结果是证明了增长定理和内部Harnack不等式。本文仅假设漂移$b$在某些Lebesgue空间中，这些空间在抛物标度下是临界的，但不一定是有界的。最后给出了内部Harnack不等式的一些应用。特别是，我们有一个“普遍的”谱间隙相关的椭圆算子。在\cite{S10}中给出了二阶一致椭圆型方程的对应的无散度形式.
Estimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials
对于右手边带有含时Radon测度的发展$p$ -Laplace方程的弱解，我们通过非线性抛物势得到了点态估计.
Singular Dirichlet boundary problems for a class of fully nonlinear parabolic equations in one dimension
本文研究一维完全非线性抛物方程的奇异 Dirichlet 初值问题，涵盖 $p$-Laplace 型热方程与曲率流，揭示解的存在性如何依赖内部方程和初值有界性。
We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all $t>0$. The singularity of these solutions is of the same type as the singularity of a stationary solution to which they converge as $t\to\infty$.
The Cauchy-Dirichlet problem for a general class of parabolic equations
我们证明了一类抛物型方程的Cauchy-狄利克雷问题的内部Lipschitz正则性和边界连续性等正则性结果，这些结果是受演化$p$ -Laplacian的启发而得到的，但在更广的范围内得到了推广.我们采用了正则化技术的粘性型，我们发现有趣的本身。
Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents
证明了$$ \left\{ \begin{array}{ll} u_t - div \mathcal{A}(x,t,\nabla u) = 0 &\quad \text{on} \ Ω\times (-T,T), \\ u = 0 &\quad \text{on} \ \partial Ω\times (-T,T), \end{array} \right. $$形式的拟线性抛物型方程的\emph{very weak}解的（空间）梯度的边界高阶可积性，其中非线性结构$\mathcal{A}(x, t,\nabla u)$是在$|\nabla u|^{p(x,t)-2} \nabla u$给出的变指数$p(x,t)$ -Laplace算子之后建模的.为此，我们证明了梯度满足逆Hölder不等式附近的边界通过构造一个合适的测试函数，这是Lipschitz连续的，并保持边界值。在$p(x,t) \geq \mathfrak{p}^- \geq 2$成立的情况下，在\cite{bogelein2014very}中证明了这一结果，并将其推广到\cite{li2017very}中的奇异情形$\frac{2n}{n+2}< \mathfrak{p}^-\leq p(x,t)\leq \mathfrak{p}^+ \leq 2$.这个限制是必要的，因为拟线性抛物问题的内在标度在$\mathfrak{…
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
Fully nonlinear parabolic equations in two space variables
证明了两个空间变量的完全非线性抛物型方程解的二阶导数的Hölder估计。相关技术扩展了高维完全非线性抛物型方程的正则性理论。
In this article, for a fourth-order parabolic equation which is closely related for example to the Cahn-Hilliard equation, we study an inverse source problem by interior data and the continuation of solution from lateral Cauchy data. Our method relies on a Carleman estimate and proves conditional stability for both problems.
Uniqueness of renormalized solutions to nonlinear parabolic problems with lower order terms
本文证明了一类非线性抛物型方程重正化解的唯一性结果。
In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove comparison principle, global existence and blow-up of solutions.
A counterexample to $C^{2,1}$ regularity for parabolic fully nonlinear equations
我们解决了奇异抛物问题的自相似可解性，并表明抛物型完全非线性方程的解决方案预计不会是$C^{2,1}$。
The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations
研究了三维不可压Navier-Stokes方程斯托克斯方程适当弱解的可能内部奇点。我们提出了一个改进的抛物上Minkowski维数的可能奇异集。它以$95/63$为界。对于三维不可压缩磁流体动力学方程组，所得结果也继续成立。
We obtain up to a flat boundary regularity results in parabolic Hölder spaces for viscosity solutions of fully nonlinear parabolic equations with oblique boundary conditions.
Blow-up of solutions for a semilinear parabolic equation with nonlinear memory and absorption under nonlinear nonlocal boundary condition
研究含非线性记忆与吸收项的半线性抛物方程在非线性非局部边界条件下的初边值问题，通过理论分析证明了解的整体存在性与有限时刻爆破。
Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case
研究一类强耦合退化抛物方程组有界弱解的Hölder正则性.
In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.
We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully nonlinear parabolic system.
Null-Controllability of 1-D parabolic equations
证明了具有时间无关可测系数的一维抛物型方程的内部零能控性。
We establish Harnack's estimates for positive weak solutions to a mixed local and nonlocal doubly nonlinear parabolic equation. All results presented in this paper are provided together with quantitative estimates.
Riesz potentials and nonlinear parabolic equations
非线性退化抛物型方程解的空间梯度可以由右侧数据的热里斯位势逐点估计，与热方程的情况完全一样。热核类型估计在非线性情况下持续存在
Asymptotic Behavior and Decay Estimates of the Solutions for a Nonlinear Parabolic Equation with Exponential Nonlinearity
考虑一类非线性抛物型方程，其指数非线性项对非线性项的增长和初值的正则性是临界的。在证明了弱解和温和解的等价性之后，我们得到了小的全局时间解的衰减估计和渐近行为。
On the strong maximum principle for fully nonlinear parabolic equations of second order
本文针对二阶完全非线性一致抛物型方程，提出一种不依赖抛物型 Harnack 不等式的抛物型证明方法，建立其强最大值原理与强最小值原理。
Boundary behavior of nonnegative solutions of fully nonlinear parabolic equations
研究了完全非线性抛物型Pucci极值算子粘性非负解的边界表现.我们建立了$C^{1，1}圆柱上的局部和整体比较定理，以及一个向后的Harnack不等式.
Uniform Regularity Estimates in Parabolic Homogenization
本文考虑一类由均匀化理论产生的具有快速振荡且系数随时间变化的散度型二阶抛物方程组。利用紧性方法，我们得到了一致的内部$W^{1,p}$，Hölder和Lipschitz估计以及边界$W^{1,p}$和Hölder估计.作为结果，我们建立了$C^{1}$柱上初始狄利克雷问题的一致$W^{1,p}$估计.
In this paper, we prove $\mathcal{H}^{2+α}$ regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic counterpart of a similar $C^{2, α}$ regularity result due to Silvestre and Sirakov proved in [15] for solutions to non-convex fully nonlinear elliptic equations.
We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order semilinear parabolic equations, and viscous Hamilton-Jacobi equations by using the majorant kernel introduced in [K. Ishige, T. Kawakami, and S. Okabe, Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), 1185--1209].
Regularity for solutions of non local parabolic equations II
证明了抛物型非局部方程$u_t-Iu=f$的边界正则性和紧性结果，其中算子$I$不一定是平移不变的.由于这一点和正则性结果的平移不变的情况下，我们得到了$C^{1,α}$内部估计空间的非平移不变运营商在一定的假设下的时间规则性的边界数据。
We present a blow-up rate estimate for a solution to the parabolic Gross-Pitaevskii and related systems on entire space with Sobolev subcritical nonlinearity. We extend the results of [Y. Giga, S. Matsui and S. Sasayama, Indiana Univ. Math. J. {53} (2004), 483--514] to the parabolic systems.
Hölder gradient estimates for parabolic homogeneous p-Laplacian equations
证明了抛物型齐次$p$ -Laplacian方程\[ u_t=|\nabla u|^{2-p} \mbox{ div} (|\nabla u|^{p-2}\nabla u), \]的黏性解的空间梯度的内Hölder估计，其中$1<p<\infty$ .这个方程来自于带噪声的类似拔河的随机对策。它也可以看作是非散度型的抛物型$p$ -Laplacian方程。
A New Stability Result for Viscosity Solutions of Nonlinear Parabolic Equations with Weak Convergence in Time
本文给出了完全非线性抛物型方程的黏性解的一个新的稳定性结果，当非线性项在时间上只有弱收敛时，该结果可以达到极限。
We investigate the existence of a renormalized solution for a class of nonlinear parabolic equations with two lower order terms and $L^1$-data.
In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge-Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of Dynamic Programming Principles for certain two-player, zero-sum games.
Higher integrability for doubly nonlinear parabolic systems
本文研究了双重非线性抛物方程组弱解空间梯度的局部更高可积性，通过引入同时涉及解及其空间梯度的内蕴几何方法进行证明，主要结果适用于特定参数范围。
In this paper we study the initial boundary value problem for the system $u_t-Δu^m=-\mbox{div}(u^{q}\nabla v),\ v_t-Δv+v=u$. This problem is the so-called Keller-Segel model with nonlinear diffusion. Our investigation reveals that nonlinear diffusion can prevent overcrowding. To be precise, we show that solutions are bounded as long as $m>q>0$, thereby substantially generalizing the known results in this area. Furthermore, our result seems to imply that the Keller-Segel model can have bounded solutions and blow-up ones simultaneously.
By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we derive consequences for fully nonlinear parabolic equations of the form $\dt v + F(t,x,D^2v)=0$, where $F$ can be both singular and degenerate elliptic and also non-homogeneous. Such equations appear in the theory of option pricing with market impact.
In this paper, we establish blow-up rates for higher-order semilinear parabolic equations with nonlocal in time nonlinearity with no positive assumption on the solution. We also give Liouville-type theorem for higher-order semilinear parabolic equation with infinite memory nonlinear term which plays the main tools to prove our blow-up rate result. Finally, we study the well-posedness of mild solutions.
A Phragmén-Lindelöf property of viscosity solutions to a class of nonlinear, possibly degenerate, parabolic equations
在$\mathbb{R}^n\times (0,T)$中研究了一类双非线性抛物型方程的黏性解的Phragmén-Lindelöf性质.我们还包括一些双非线性方程的应用。
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。