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Serrin-type Overdetermined problems in $\mathbb H^n$
- Publication Year :
- 2022
-
Abstract
- In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $\sigma_k(D^2u-uI)=C_n^k$ in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.
- Subjects :
- Mathematics - Analysis of PDEs
35N25, 35B06, 35B50, 53C24
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2201.04323
- Document Type :
- Working Paper