Related papers: Lyapunov inequalities for Neumann boundary conditi…

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincar\'e inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite simple and efficient technique:…

For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component…

We consider the equation $-\epsilon^{2}\Delta u + u = u^ {p}$ in a bounded domain $\Omega\subset\R^{3}$ with edges. We impose Neumann boundary conditions, assuming $1<p<5$, and prove concentration of solutions at suitable points of…

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…

We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…

Let $M$ be a compact Riemannian manifold with boundary $\pp M$ and $L= \DD+Z$ for a $C^1$-vector field $Z$ on $M$. Several equivalent statements, including the gradient and Poincar\'e/log-Sobolev type inequalities of the Neumann semigroup…

We study Neumann type boundary value problems for nonlocal equations related to L\'evy processes. Since these equations are nonlocal, Neumann type problems can be obtained in many ways, depending on the kind of reflection we impose on the…

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint…

In this paper, we study the first eigenvalue of the magnetic Laplacian with Neumann boundary conditions in the unit disk $\mathbb D$ in $\mathbb R^2$. There is a rather complete asymptotic analysis when the constant magnetic field tends to…

This paper deals with fractional Sobolev spaces on a compact Riemannian manifold. We prove a Sobolev inequality in the critical range with an optimal constant for these fractional Sobolev spaces. We use this result to study the existence of…

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the…

In this note we present upper bounds for the variational eigenvalues of the $p$-Laplacian on smooth domains of complete $n$-dimensional Riemannian manifolds and Neumann boundary conditions, and on compact (boundaryless) Riemannian…

In \cite{cheung2019optimally}, the authors presented two finite element methods for approximating second order boundary value problems on polytopial meshes with optimal accuracy without having to utilize curvilinear mappings. This was done…

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…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

This paper deals with a priori pointwise error estimates for the finite element solution of boundary value problems with Neumann boundary conditions in polygonal domains. Due to the corners of the domain, the convergence rate of the…

We study a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains $\Omega\subset \mathbb{R}^{N} $, $N\ge1$, under Robin boundary conditions, proving the existence of two positive eigenvalues $\lambda^{\pm}$…

In this article, we show that prescribing homogeneous Neumann type numerical boundary conditions at an outflow boundary yields a convergent discretization in $\ell^\infty$ for transport equations. We show in particular that the Neumann…

We consider the Neumann problem $$(P)\qquad - \Delta v + v= v^{q-1} \ \text{in }\ \mathcal{D}, \ v > 0 \ \text{in } \ \mathcal{D},\ \partial_\nu v = 0 \ \text{on } \partial\mathcal{D} ,$$ where $\mathcal{D} $ is an open bounded domain in…

We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. Our main result…