Related papers: Eigenvalue Estimates for $p$-Laplace Problems on D…

In this paper, we prove the existence of a family of non trivial compact subdomains $\O$ in the manifold $\mathcal{M}=\R^N\times \R/2\pi\Z, N\geq 2$ for which the overdetermined Neumann boundary value problem \begin{align}\label{Neumann1}…

We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of…

Simultaneous measurements of position and momentum are considered in $n$ dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty…

We present asymptotically sharp inequalities for the eigenvalues $\mu_k$ of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in \cite{HaSt14}. For the Riesz mean $R_1(z)$ of the…

This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the…

We consider weighted p-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp…

Here we prove an isoperimetric inequality for the harmonic mean of the first $N-1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of $\mathbb{S}^N$.

We present a new and direct proof of the local Neumann isoperimetric inequality on convex domains of a Riemannian manifold with Ricci curvature bounded below.

In this manuscript, we study the nonlinear eigenvalue problem on complete Riemannian manifolds with Ricci curvature bounded from below, to find the unknowns $\lambda$ and $u$, such that $$ Qu + \lambda f(u) = 0 $$ where $\lambda$ is an…

We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel…

We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…

We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterised by…

Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neumann eigenvalues of the submanifolds when they converge in the…

This paper studies a class of $p$-Laplace equations with cubic polynomial nonlinearity \[ \Delta_p v + (v-a_1)(v-a_2)(v-a_3) = 0 \] on complete Riemannian manifolds $M$ with lower Ricci curvature bounds, where $a_1 < a_2 < a_3$ are real…

Consider the Laplacian in a bounded domain in R^d with general (mixed) homogeneous boundary conditions. We prove that its eigenfunctions are `quasi-orthogonal' on the boundary with respect to a certain norm. Boundary orthogonality is proved…

We consider the problem of minimising the $k$-th eigenvalue of the Laplacian with some prescribed boundary condition over collections of convex domains of prescribed perimeter or diameter. It is known that these minimisation problems are…

We will present an estimate for the first eigenvalue of the Dirichlet and Neumann problems in terms of the Bakry-\'Emery Ricci curvature for a compact weighted manifold. As an application we will establish a stability condition for a…

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…

If the boundary of a domain in three dimensions is smooth enough, then the decay rate of the eigenvalues of the Neumann-Poincar\'e operator is known and it is optimal. In this paper, we deal with domains with less regular boundaries and…

We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of…