Related papers: Eigenvalues homogenization for the fractional $p-$…

We give a short proof of simplicity of the eigenvalues of the fractional Laplace operator in an interval, a result shown recently by Fall, Ghimenti, Micheletti and Pistoia [Calc. Var. Partial Differ. Equ. 62 (2023), #233].

In this paper, we will study Neumann $(p,q)$-eigenvalue problem for the weighted $p$-Laplace operator in outward H\"older cuspidal domains. The suggested method is based on the composition operators on weighted Sobolev spaces.

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a…

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way…

In this paper, we study eigenvalue of linear fourth order elliptic operators in divergence form with Dirichlet boundary condition on a bounded domain in a compact Riemannian manifolds with boundary (possibly empty) and find a general…

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

This paper investigates the first Dirichlet eigenvalue for the $p$-Laplacian in Riemannian manifolds. Firstly, we establish a lower bound for this eigenvalue under the condition that the domain includes a specific function which fulfills…

In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…

The spectral properties of the restricted fractional Laplacian with Dirichlet boundary conditions in a smoothly bent waveguide is investigated. The existence of eigenvalues below the threshold of the continuous spectrum is proved,…

We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…

We investigate quantitative estimates in homogenization of the locally periodic parabolic operator with multiscales $$ \partial_t- \text{div} (A(x,t,x/\varepsilon,t/\kappa^2) \nabla ),\qquad \varepsilon>0,\, \kappa>0. $$ Under proper…

The elastic Neumann--Poincar\'e operator is a boundary integral operator associated with the Lam\'e system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two…

We study the eigenvalue problem for the $g-$Laplacian operator in fractional order Orlicz-Sobolev spaces, where $g=G'$ and neither $G$ nor its conjugated function satisfy the $\Delta_2$ condition. Our main result is the existence of a…

We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and only if…

The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type of characterization for the fractional powers of second order partial differential…

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…

We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang \cite{NiuZhang} for the…

We study the eigenvalue problem for the $p$-Laplacian on K\"ahler manifolds. Our first result is a lower bound for the first nonzero eigenvalue of the $p$-Laplacian on compact K\"ahler manifolds in terms of dimension, diameter, and lower…

We obtain asymptotic estimates for the eigenvalues of the p(x)-Laplacian defined consistently with a homogeneous notion of first eigenvalue recently introduced in the literature.

In this paper,we will study the homogenization of $p$-Laplacian with obstacles in perforated domain, where the holes are periodically distributed and have random size. And we also assume that the $p$-capacity of each hole is stationary…