2023/06/21 by De Nitti, Nicola, Sakaguchi, Shigeru
#35B06 #35B35 #35J86 #35N25 #35R35 #49J40 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.12124
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem 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.