Related papers: On the first Robin eigenvalue of a class of anisot…

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular…

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…

Let $M$ be an $n$-dimensional closed Riemannian manifold with metric $g$, $d\mu=e^{-\phi(x)}d\nu$ be the weighted measure and $\Delta_{p,\phi}$ be the weighted $p$-Laplacian. In this article we will investigate monotonicity for the first…

We establish the monotonicity of the principal eigenvalue $\lambda_1(A)$, as a function of the advection amplitude $A$, for the elliptic operator $L_{A}=-\mathrm{div}(a(x)\nabla)+A\mathbf{V}\cdot\nabla +c(x)$ with incompressible flow…

Let $\Omega$ be a bounded, connected, sufficiently smooth open set, $p>1$ and $\beta\in\mathbb R$. In this paper, we study the $\Gamma$-convergence, as $p\rightarrow 1^+$, of the functional \[ J_p(\varphi)=\frac{\int_\Omega F^p(\nabla…

This paper deals with eigenelements of the Laplacian in bounded domains, under Robin boundary conditions, without any assumption on the sign of the Robin parameter. We quantify the asymptotics of the variation of simple eigenvalues under…

This paper addresses the geometric optimization problem of the first Robin eigenvalue in exterior domains, specifically the lowest point of the spectrum of the Laplace operator under Robin boundary conditions in the complement of a bounded…

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue $\mu_1(\Omega)$ for the $p$-Laplace operator in a Lipschitz, bounded domain $\Omega$ in $\R^n$. Our estimate does not require any convexity assumption on…

We consider a class of quasilinear operators on a bounded domain $\Omega\subset \mathbb R^n$ and address the question of optimizing the first eigenvalue with respect to the boundary conditions, which are of the Robin-type. We describe the…

We consider Robin Laplace operators on a class of two-dimensional domains with cusps. Our main results include the formula for the asymptotic distribution of the eigenvalues of such operators. In particular, we show how the eigenvalue…

Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with $\beta\in\R\setminus\{0\}$ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if $\beta>0$ and a shape…

We compute the sum and number of eigenvalues for a certain class of magnetic Schrodinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the…

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic…

We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this framework, since the convergence of the Robin eigenvalues to…

We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…

On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions.…

The spectral theory of the p-Laplacian is well developed for classical Dirichlet and Neumann boundary conditions, but the transitional Robin regime on exterior domains remains largely unexplored. This paper studies a weighted p-Laplacian…

We investigate the effect of frequency on the principal eigenvalue of a time-periodic parabolic operator with Dirichlet, Robin or Neumann boundary conditions. The monotonicity and asymptotic behaviors of the principal eigenvalue with…

We give a counterexample to the long standing conjecture that the ball maximises the first eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the same volume. Furthermore, we show that the conjecture holds…

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…