相关论文: On the asymptotic behavior of $p$-fractional eigen…

The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic…

We investigate the spectral properties of the Steklov problem for the modified Helmholtz equation $(p-\Delta) u = 0$ in the exterior of a compact set, for which the positive parameter $p$ ensures exponential decay of the Steklov…

In this paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…

We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary H\"older continuity of the solutions of related Dirichlet problems. Then, we present some applications…

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…

This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…

We consider the Laplacian eigenvalues for smooth planar domains with strongly attractive Robin conditions imposed on a part of the boundary and Neumann condition on the remaining boundary. The asymptotics of individual eigenvalues is…

We study eigenvalues of general scalar Dirichlet polyharmonic problems in domains in $\mathbb R^{d}$. We first prove a number of inequalities satisfied by the eigenvalues on general domains, depending on the relations between the orders of…

We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the…

We provide a full series expansion of a generalization of the so-called $u$-capacity related to the Dirichlet-Laplacian in dimension three and higher, extending previous results of the authors, and of the authors together with Virginie…

We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak…

We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in domains with conic singularities and establish asymptotic expansions with respect to two normal directions simultaneously. The spherical domains over which cones…

We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a non-uniform magnetic field having a jump discontinuity…

Let $f(n)$ be an arithmetic function with $f(1)\neq0$ and let $f^{-1}(n)$ be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behaviour of $|f^{-1}(n)|$ with regard to the asymptotic behaviour of $|f(n)|$…

In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded planar domain. We establish a sharp relation between the rate of…

This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized…

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 introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first $k$ Dirichlet eigenvalues of the fractional…

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…

We consider the spectrum of the Laplace operator on 3D rod structures, with a small cross section depending on a small parameter $\varepsilon$. The boundary conditions are of Dirichlet type on the basis of this structure and Neumann on the…