Elliptic and parabolic overdetermined problems in multi-phase settings
Analysis of PDEs
2025-05-27 v2
Abstract
The present paper provides symmetry results for a class of overdetermined problems of elliptic and parabolic type in multi-phase settings, including various extensions of remarkable results obtained by S. Sakaguchi in [12, 13]. A new alternative approach to proving this type of results is presented, leveraging the weak formulation of the problem. The resulting proofs are direct and elegant, and bring several benefits, including extensions to multi-phase settings (possibly with infinitely many phases) and generalizations to rough interfaces.
Keywords
Cite
@article{arxiv.2504.18808,
title = {Elliptic and parabolic overdetermined problems in multi-phase settings},
author = {Lorenzo Cavallina and Giorgio Poggesi},
journal= {arXiv preprint arXiv:2504.18808},
year = {2025}
}
Comments
21 pages, 2 figures