English

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

R2 v1 2026-06-28T23:12:09.417Z