Some elliptic PDEs on Riemannian manifolds with boundary
Yannick Sire, Enrico Valdinoci
TL;DR
This paper explores the rigidity properties of stable solutions to elliptic PDEs on Riemannian manifolds with boundary, considering effects of manifold dimension and Ricci curvature.
Contribution
It provides new rigidity results for stable solutions of elliptic equations on manifolds with boundary, depending on geometric conditions.
Findings
Rigidity results vary with manifold dimension.
Results depend on the sign of Ricci curvature.
New conditions for stability of solutions.
Abstract
The goal of this paper is to investigate some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. We provide several types of results, according to the dimension of the manifold and the sign of its Ricci curvature.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering