Related papers: Pointwise gradient bounds for entire solutions of …
We consider fully nonlinear degenerate elliptic equations with zero and first order terms. We provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which…
This note studies local integral gradient bounds for distributional solutions of a large class of partial differential inequalities with diffusion in divergence form and power-like first-order terms. The applications of these estimates are…
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
This paper studies a new gradient regularity in Lorentz spaces for solutions to a class of quasilinear divergence form elliptic equations with nonhomogeneous Dirichlet boundary conditions: \begin{align*} \begin{cases} div(A(x,\nabla u)) &=…
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
In this work we establish a gradient bound and Liouville-type theorems for solutions to Quasi-linear elliptic equations on compact Riemannian Manifolds with nonnegative Ricci curvature. Also, we provide a local splitting theorem when the…
We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach…
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…
Smoothness of generalized solutions for higher-order elliptic equations with nonlocal boundary conditions is studied in plane domains. Necessary and sufficient conditions upon the right-hand side of the problem and nonlocal operators under…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…
In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the constant branch determined by a critical point of the potential,…
In this paper, we study fully nonlinear second-order elliptic and parabolic equations with Neumann boundary conditions on compact Riemannian manifolds with smooth boundary. We derive oscillation bounds for admissible solutions with Neumann…
We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak…
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered:…