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We give blow-up behavior for solutions to an elliptic system with Dirichlet condition, and, weight and boundary singularity. Also, we have a compactness result for this elliptic system with regular H{\"o}lderian weight and boundary…

Analysis of PDEs · Mathematics 2019-01-25 Samy Skander Bahoura

We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…

Analysis of PDEs · Mathematics 2022-07-01 Cristiana De Filippis , Mirco Piccinini

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…

Analysis of PDEs · Mathematics 2007-05-23 Marie-Francoise Bidaut-Veron , Rouba Borghol , Laurent Veron

In this paper we are concerned with the regularity of solutions to a nonlinear elliptic system of $m$ equations in divergence form, satisfying $p$ growth from below and $q$ growth from above, with $p \leq q$; this case is known as $p,…

Analysis of PDEs · Mathematics 2021-08-27 G. Cupini , F. Leonetti , E. Mascolo

We give a blow-up analysis and a compactness result for an equation with Holderian condition and boundary singularity.

Analysis of PDEs · Mathematics 2018-06-12 Samy Skander Bahoura

The paper concerns singular solutions of nonlinear elliptic equations.

Analysis of PDEs · Mathematics 2009-04-21 Luis Caffarelli , YanYan Li , Louis Nirenberg

In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which…

Analysis of PDEs · Mathematics 2011-05-16 Dragos-Patru Covei

We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product we obtain a new stability estimate in the linear case. We also show the…

Analysis of PDEs · Mathematics 2022-08-18 Mourad Choulli

In this survey paper, we study the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains and establish the H\"older continuity of solutions and their derivatives up to the boundary.

Analysis of PDEs · Mathematics 2024-11-26 Qing Han , Jiongduo Xie

We study mixed local and nonlocal elliptic equation with a variable coefficient $\rho$. Under suitable assumptions on the behaviour at infinity of $\rho$, we obtain uniqueness of solutions belonging to certain weighted Lebsgue spaces, with…

Analysis of PDEs · Mathematics 2023-07-06 Stefano Biagi , Giulia Meglioli , Fabio Punzo

We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…

Analysis of PDEs · Mathematics 2025-03-14 Mourad Choulli , Hiroshi Takase

This paper provides results for eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric…

Analysis of PDEs · Mathematics 2017-05-22 M. A. Rivas , Stephen B. Robinson

Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift

Analysis of PDEs · Mathematics 2019-04-09 Yongpan Huang

Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of a solution to a mixed boundary condition linear eigenvalue…

Analysis of PDEs · Mathematics 2016-08-10 Lucio Damascelli , Filomena Pacella

An elliptic divisibility sequence, generated by a point in the image of a rational isogeny, is shown to possess a uniformly bounded number of prime terms. This result applies over the rational numbers, assuming Lang's conjecture, and over…

Number Theory · Mathematics 2015-05-13 Graham Everest , Patrick Ingram , Valery Mahe , Shaun Stevens

This paper investigates the local boundedness of weak solutions to a direction-dependent double-phase nonlocal elliptic equation. By employing refined energy estimates and De Giorgi-type techniques, we establish the local boundedness of…

Analysis of PDEs · Mathematics 2026-02-16 Hamid El Bahja

We consider variational problems with regular H{\"o}lderian weight or boundary singularity, and Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on analytic domains.

Analysis of PDEs · Mathematics 2023-08-02 Samy Skander Bahoura

We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.

Analysis of PDEs · Mathematics 2012-05-23 Panagiota Daskalopoulos , Tuomo Kuusi , Giuseppe Mingione

In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varying characteristic exponents.

Analysis of PDEs · Mathematics 2024-11-27 Qing Han , Jiongduo Xie

In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.

General Relativity and Quantum Cosmology · Physics 2015-06-25 Sergio Dain