Overdetermined problems and constant mean curvature surfaces in cones
By Filomena Pacella, G. Tralli. Revista matemática iberoamericana, 2018
47 citations recorded by the source corpus.
We consider a partially overdetermined problem in a sector-like domain $\Omega$ in a cone $\Sigma$ in $\mathbb{R}^N$, $N\geq 2$, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that $\Omega$ is a spherical sector, under a convexity assumption on the cone. We also consider the related question of characterizing constant mean curvature compact surfaces $\Gamma$ with boundary which satisfy a "gluing" condition with respect to the cone $\Sigma$. We prove that if either the cone is convex or the surface is a radial graph then $\Gamma$ must be a spherical cap. Finally we show that, under the condition that the relative boundary of the domain or the surface intersects orthogonally the cone, no other assumptions are needed.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a6446bcb1d05e96c2cba8c77cffaace52aca8add
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In Applied Mathematics
- Alessio Figalli
- Giulio Ciraolo
- A. Roncoroni
- Guido De Philippis
- Max Fathi
- Dario Trevisan
- Robert J. McCann
- N. Fusco
In Computational Theory and Mathematics
Citations in the corpus
- Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019, background): “an equations, which is based on integral identities rather than moving planes. This approach takes inspiration from [5, 6, 7] where classical overdetermined problems for PDEs are considered (see also [13, 29] for analogous problems in convex cones). Strategy of the proof and structure of the paper. ”