Related papers: Estimates for eigenvalues of the Neumann and Stekl…

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…

In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and quaternionic projective spaces. We also prove similar results…

Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Writing his approach in terms of…

We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric…

In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded…

We investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the Laplacian on Euclidean domains of unit volume, under Dirichlet and Neumann boundary conditions, respectively. In a second part,…

In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an $n$-dimensional Riemannian manifold.

We establish inequalities for the eigenvalues of Schr\"odinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related…

We use layer potential to establish that the boundary biharmonic Steklov operators are elliptic pseudo-differential operators. Thus we are able to establish lower bounds on both the measure of boundary nodal sets and interior nodal sets for…

We prove two upper bounds for the Steklov eigenvalues of a compact Riemannian manifold with boundary. The first involves the volume of the manifold and of its boundary, as well as packing and volume growth constants of the boundary and its…

We consider the Neumann problem in $C^2$ bounded domains for fully nonlinear second order operators which are elliptic, homogenous with lower order terms. Inspired by \cite{bnv}, we define the concept of principal eigenvalue and we…

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 derive sharp bounds for three types of eigenvalue problems. First, we derive an upper bound for the first $p$-Dirichlet eigenvalue on conformally compact (CC) spaces. As a consequence, we show that for a class of CC submanifolds of…

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the…

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 consider a compact Riemannian manifold M endowed with a potential 1-form A and study the magnetic Laplacian associated with those data (with Neumann magnetic boundary condition if the bpoundary of M is not empty). We first establish a…

We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the…

In this paper, we establish Brezin-Li-Yau type lower bounds for averaged sums of Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded domains in Euclidean spaces. By deriving expansions of two binary polynomials which may be…

Let $\Omega$ be a bounded domain with $C^\infty$ boundary in an $n$-dimensional $C^\infty$ Riemannian manifold, and let $\varrho$ be a non-negative bounded function defined on $\partial \Omega$. It is well-known that for the biharmonic…

In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…