Related papers: Strong unique continuation and local asymptotics a…
We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…
We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asymptotically linear problem in general domains. Furthermore, we…
We study the quantitative unique continuation on the boundary for solutions of elliptic equations with Neumann boundary conditions for bounded potentials and boundary potentials on compact manifolds with boundary. The boundary doubling…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
In this article, we study the boudary blow-up solutions for semilinear fractional equations with power absorption. Our main purpose is to obtain the existence, nonuniqueness and behavior asymptotic near the boundary.
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations…
In this paper, the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain is studied. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary whereas the…
In this paper we prove the boundedness and H\"older continuity of quasilinear elliptic problems involving variable exponents for a homogeneous Dirichlet and a nonhomogeneous Neumann boundary condition, respectively. The novelty of our work…
In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…
We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption…
The asymptotic behavior of solutions to Schr\"odinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the…
We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are…
In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an isolated singularity. In particular, we prove a uniqueness of…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool…
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…
We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of coupled nonlinearities with asymptotic critical behaviour in…
This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…
In this paper we establish the \emph{space-like} strong unique continuation for nonlocal equations of the type $(\partial_t - \Delta)^s u= Vu$, for $0<s <1$. The proof of our main result, Theorem 1.1, is achieved via a conditional elliptic…