Norayr Matevosyan, Peter Markowich
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.
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
On One Generalization of the Multipoint Nonlocal Contact Problem for Elliptic Equation in Rectangular Area
本文研究矩形区域内椭圆方程的多点非局部接触问题，提出分离变量法和迭代法求解，并证明解的存在唯一性。
This paper is concerned with the nonlinear elliptic problem $-Δu=\frac{λ}{(a-u)^2}$ on a bounded domain $Ω$ of $\mathbb{R}^N$ with Dirichlet boundary conditions. This problem arises from Micro-Electromechanical Systems devices in the case that the elastic membrane contacts the ground plate on the boundary. We analyze the properties of minimal solutions to this equation when $λ>0$ and the function $a:\barΩ\to[0,1]$ satisfying $a(x)\ge κ{\rm dist}(x,\partialΩ)^γ$ for some $κ>0$ and $γ\in(0,1)$. Our results show how the boundary decay of the membrane works on the solutions and pull-in voltage $λ$…
In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic equations arising from a Yamabe problem with boundary and reflector problems.
On the justification of Koiter's model for elliptic membranes subjected to an interior normal compliance contact condition
本文严格证明了受内部法向柔性接触条件的线性弹性椭圆薄膜壳 Koiter 模型的合理性，通过建立新的密度结果并利用特设公式证明二维障碍问题解的横向分量迹的适定性与更高正则性。
Course Notes on Nonlinear Partial Differential Equations of Elliptic Type given to Master students at the University of Craiova, Romania.
We classify homogeneous degree $d\neq2$ solutions to fully nonlinear elliptic equations.
Subsonic flows with a contact discontinuity in a two-dimensional finitely long curved nozzle
研究二维有限长轻微弯曲喷管中带接触间断的亚音速流，借助 Lagrange 变换、加权 Hölder 空间估计与隐函数定理证明其存在唯一性。
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.
We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth ($C^\infty$) solutions.
We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive viscosity solutions.
Boundedness and blow-up of solutions for a nonlinear elliptic system arising in probability and stochastic processes
We prove that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally $C^{1,γ}$-regular.
A Visual Approach to the Regularity Theory for Fully Nonlinear Elliptic Equations
本文通过视觉方法重新审视一致椭圆方程的正则性理论，旨在提供直观理解。
We prove global Holder estimates for solution of fully nonlinear elliptic or degenerate elliptic equations in unbounded domains under geometric conditions on the domain a' la Cabre'.
We establish some existence results for a class of critical elliptic problems with singular exponential nonlinearities. We do not assume any global sign conditions on the nonlinearity, which makes our results new even in the nonsingular case.
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
In this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and $L^{1}$ datum in the setting of variable exponent Sobolev spaces. We will prove that the lower order term has some regularizing effects on the solutions. This work generalizes some results given in \cite{1}.
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a solution of a suitable homogeneous nonlinear elliptic equation associated to an operator with nonstandard growth.
Schauder-type estimates for fully nonlinear degenerate elliptic equations
该文针对完全非线性退化椭圆方程，研究其解在内部源项消失点处的正则性，得到了依赖类Hölder源项-椭圆性消失速率的Schauder型正则性估计。
We find a solution of a quasilinear elliptic equation with Dirichlet's boundary condition on a smooth bounded domain and involving an unbounded continuous nonlinearity with oscillatory behavior near the origin.
In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.
We show that in dimension 3 axial-symmetric viscosity solutions of uniformly elliptic Hessian equations are in fact the classical ones.
We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.
Solutions to the nonlinear obstacle problem with compact contact sets
本文通过建立全局解与描述渐近行为的二次多项式之间的双射，完整刻画了非线性障碍问题中具有紧接触集的解空间。
We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such as the Yamabe equation, Hardy-Hénon equation etc.
Dirichlet problem for a class of nonlinear degenerate elliptic operators with critical growth and logarithmic perturbation
该研究聚焦于一类带临界增长与对数扰动的非线性退化椭圆算子的Dirichlet问题，探究其弱解的存在性。
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions to the 2-d Euler equation, and analyticity of water waves with and without surface tension.
We establish an optimal C^{1,α}-regularity for viscosity solutions of degenerate/singular fully nonlinear elliptic equations by finding minimal regularity requirements on the associated operator.
Interior $C^{2,α}$ regularity for fully nonlinear uniformly elliptic equations in dimension two
本文研究了二维全非线性均匀椭圆方程粘性解的内部$C^{2,α}$正则性问题。
In this paper, we establish a global $C^2$ estimates to the Neumann problem for a class of fullly nonlinear elliptic equations. By the method of continuity, we establish the existence theorem of $k$-admissible solutions of the Neumann problems.
We consider the nonlinear Schrödinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schrödinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent
本文利用变分方法研究一类涉及混合卷积型和Hardy非线性的非线性椭圆问题，探讨亚临界和临界增长下的解的存在性。
In this paper, we use variational methods to prove the existence of positive solution for the following class of elliptic equation $$ -ε^{2}Δ{u}+V(z)u=f(u) \,\,\, \mbox{in} \,\,\, \mathbb{R}^{2}, $$ where $ε>0$ is a positive parameter, $V$ is a saddle-like potential and $f$ has an exponential critical growth.
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurcation for a class of singular elliptic problems with subquadratic convection term. In some concrete situations we also establish the asymptotic behaviour of the solution around the bifurcation point. Our …
We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and in modulation spaces are obtained. In one spatial dimension, we get the sharp well posedness result with small data in critical homogeneous Besov spaces. As a by-product, the existence of the scattering operators with small data is also shown. In order to show these results, the global versions of the estimates for the maximal functions on the elliptic and no…
We obtain an error estimate between viscosity solutions and δ-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is Lipschitz-continuous in space with linear growth in the Hessian. We also establish a rate of convergence for monotone and consistent finite difference approximation schemes for such equations.
In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for linear equations. The geometrical conditions in this paper are pointwise and more general than before. Moreover, our proofs are relatively simple.
We will study solvability of nonlinear second-order elliptic system of partial differential equations with nonlinear boundary conditions. We study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the spectral parameter is both in the system and on the boundary. We prove the existence of solutions for nonlinear system when both nonlinearities in the differential system and on the boundary interact, in some sense, with the generalized spectrum of Steklov Robin. The method of proof makes use of Leray-Schauder degree.
We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions constructed from the fundamental solution of the linearized problem.
We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in divergence form.
We consider the uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities. We deduce the uniqueness from the argument in the classical paper by Peletier and Serrin, thereby recovering a part of the uniqueness result of Ouyang and Shi.
We prove a $C^{1,α}$ interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity of a special class of nonlinear operators.
Liouville theorems for fully nonlinear elliptic equations on half spaces
本文通过边界正则性、Hopf和Carleson估计，简洁证明了半空间上全非线性椭圆方程的两个Liouville定理。
We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carathéodory's function. The existence theorem has been proved.
In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an application to intergo-differential problems.
Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class of quadratic functionals inducing harmonic maps.
We study the asymptotic behaviour of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of the ball, while a suitable associated energy remains invariant.
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena occurs precisely in the first Steklov eigenvalue problem. In all results we use Variational Methods, Critical Groups and the Morse Theory.
We prove weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.
We prove the symmetry of components and some Liouville-type theorems for, possibly sign changing, entire distributional solutions to a family of nonlinear elliptic systems encompassing models arising in Bose-Einstein condensation and in nonlinear optics. For these models we also provide precise classification results for non-negative solutions. The sharpness of our results is also discussed.
In this paper, we study the exterior Dirichlet problem for the fully nonlinear elliptic equation $f(λ(D^{2}u))=1$. We obtain the necessary and sufficient conditions of existence of radial solutions with prescribed asymptotic behavior at infinity.
We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order $σ\in (0,2)$ with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a refined $C^{σ+α}$ estimate in [8].
We prove that the existence of a solution to a fully nonlinear elliptic equation in a bounded domain $Ω$ with an overdetermined boundary condition prescribing both Dirichlet and Neumann constant data forces the domain $Ω$ to be a ball. This is a generalization of Serrin's classical result from 1971.
In this article we find the equivalent conditions to assure the existence and uniqueness of positive solutions to semilinear elliptic equations wih double power nonlinearities. As a bonus, we give a simpler proof of our former result that the uniqueness condition comes from the existence condition.
In this short note, the simplicity of the first eigenvalue of a nonlinear system is shown by an alternative proof; thereby, it states that the first eigenfunctions are unique up to modulo scaling.
In this note we complete the study made in a previous paper on a Kirchhoff type equation with a Berestycki-Lions nonlinearity. We also correct Theorem 0.6 inside.
Existence for noncoercive nonlinear elliptic equations with two lower-order terms
本文针对系数属于Marcinkiewicz和Lorentz空间的非强制非线性椭圆方程，证明了Dirichlet问题解的存在性，并研究了解的高阶可积性。
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to satisfy Landesman-Lazer conditions or the monotonicity assumption. The nonlinearity may be unbounded. The nonlinearity interact, in some sense with the Steklov spectrum on boundary nonlinearity. The proofs are based on a priori estimates for possible solutions to a homotopy on suitable trace and topological degree arguments.
We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth.
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。