2025/04/26 by Lorenzo Cavallina, Cavallina, Lorenzo, Giorgio Poggesi +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2504.18808
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.