相关论文: Comparison results for solutions of Poisson equati…
In this article, we establish a $L^1$ estimate for solutions to Poisson equation with mixed boundary condition, on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature…
In this paper, we obtain the Bossel-Daners inequality for the first eigenvalue of the p-Laplacian with Robin boundary conditions on complete Riemannian manifolds with lower Ricci curvature bounds. Furthermore, we demonstrate that the…
In this article, we prove Talenti's comparison theorem for Poisson equation on complete noncompact Riemannian manifold with nonnegative Ricci curvature. Furthermore, we obtain the Faber-Krahn inequality for the first eigenvalue of Dirichlet…
The purpose of this paper is to establish a quantitative version of the Talenti comparison principle for solutions to the Poisson equation with Robin boundary conditions. This quantitative enhancement is proved in terms of the asymmetry of…
We prove an existence result for the Poisson equation on non-compact Riemannian manifolds satisfying weighted Poincar\'e inequalities outside compact sets. Our result applies to a large class of manifolds including, for instance, all…
In this paper we consider PDE's problems involving the anisotropic Laplacian operator, with Robin boundary conditions. By means of Talenti techniques, widely used in the last decades, we prove a comparison result between the solutions of…
In this paper we study the $p$-Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we provide various sharp bounds for the solutions to the problems…
Let $\Omega \subset \mathbb{R}^n$ be an open, bounded and Lipschitz set. We consider the Poisson problem for the $p-$Laplace operator associated to $\Omega$ with Robin boundary conditions. In this setting, we study the equality case in the…
In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the results obtained in arXiv:1909.11950 to the case of p-Laplace…
In this article, we prove a sharp estimate for the solutions to parabolic equations on manifolds. Precisely, using symmetrization techniques and isoperimetric inequalities on Riemannian manifold, we obtain a Bandle's comparison on complete…
Given a Riemannian spin^c manifold whose boundary is endowed with a Riemannian flow, we show that any solution of the basic Dirac equation satisfies an integral inequality depending on geometric quantities, such as the mean curvature and…
We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particular we can allow the Ricci curvature to be unbounded from…
In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform…
In the first part of the article we develop a comparison method for positive solutions of the semilinear Dirichlet problem $\Delta u+f(u)=0$ on domains $\Omega\subset \mathcal M^n$ of a Riemannian manifold $(\mathcal{M}^n,g)$ with a Ricci…
In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function $f$ has decay $f=O(r^{-1-\varepsilon}) $ for…
In this paper we provide some local and global splitting results on complete Riemannian manifolds with nonnegative Ricci curvature. We achieve the splitting through the analysis of some pointwise inequalities of Modica type which hold true…
We present multiplicity results for mass constrained Allen-Cahn equations on a Riemannian manifold with boundary, considering both Neumann and Dirichlet conditions. These results hold under the assumptions of small mass constraint and small…
In this paper, we generalize a classical comparison result for solutions to Hamilton-Jacobi equations with Dirichlet boundary conditions, to solutions to Hamilton-Jacobi equations with non-zero boundary trace. As a consequence, we prove the…
The difference of the resolvents of two Laplacians on a half-space subject to Robin boundary conditions is studied. In general this difference is not compact, but it will be shown that it is compact and even belongs to some…
We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions. The method is based on a geometric formula of Poincar\'e type, which is inspired by a classical…