Serrin-type Overdetermined problems in $\mathbb H^n
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...
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| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.2201.04323 |