We establish symmetry results for two categories of overdetermined obstacle problems: Serrin-type problems and problems for two-phase conductors under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the method of moving planes; instead, it leverages the comparison principle and the fact that the solution of the obstacle problem is superharmonic within its domain. The second proof utilizes a suitable version of Serrin’s method of moving planes.
Symmetry results for some overdetermined obstacle problems
De Nitti N
;
2025-01-01
Abstract
We establish symmetry results for two categories of overdetermined obstacle problems: Serrin-type problems and problems for two-phase conductors under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the method of moving planes; instead, it leverages the comparison principle and the fact that the solution of the obstacle problem is superharmonic within its domain. The second proof utilizes a suitable version of Serrin’s method of moving planes.File in questo prodotto:
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