Related papers: Eigenvalue, maximum principle and regularity for f…

For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an…

This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear degenerate or singular uniformly elliptic equations posed in a punctured ball, in presence of a singular…

In the theory of non-linear parabolic and elliptic partial differential equations, the notion of maximal regularity plays an essential role in establishing existence, regularity and boundedness of solutions. There is a long history of works…

In this paper, we consider a generalized polyharmonic eigenvalue problem of the form $A(u)= \lambda h(u)$ in a bounded smooth domain with Dirichlet boundary conditions in the setting of higher-order Orlicz-Sobolev spaces. Here, $A$ is a…

In terms of layer potential methods, this paper is devoted to study the $L^2$ boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in a periodic setting. Under a low regularity assumption on…

We study an {\it indefinite weighted eigenvalue problem} for an operator of {\it mixed-type} (that includes both the classical {\it $p$-Laplacian} and the {\it fractional $p$-Laplacian}) in a bounded open subset $\Omega\subset \mathbb{R}^N…

This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we…

We consider elliptic operators with measurable coefficients and Robin boundary conditions on a bounded domain $\Omega \subset \mathbb{R}^d$ and show that the first eigenfunction $v$ satisfies $v(x) \ge \delta > 0$ for all $x \in…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…

In this paper we are interested in the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro-magnetism. More precisely, we study the…

The ordered eigenvalues define a Lipschitz map on the real vector space of Hermitian $d \times d$ matrices. We prove that this map acts continuously, but not uniformly continuously, by superposition on the Sobolev spaces $W^{1,q}$, for all…

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge-Amp\`ere operator on a bounded strongly pseudoconvex domain in $\C^n$. We show that the eigenfunction is…

In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…

In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…

The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators" defined as continuous superpositions of operators of…

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions or combinations of either for different parts…

This paper studies the eigenvalue problem on $\mathbb{R}^d$ for a class of second order, elliptic operators of the form $\mathscr{L} = a^{ij}\partial_{x_i}\partial_{x_j} + b^{i}\partial_{x_i} + f$, associated with non-degenerate diffusions.…

We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…