Preprint
Inserted: 21 jul 2026
Last Updated: 21 jul 2026
Year: 2026
Abstract:
We study Serrin-type overdetermined problems for a class of possibly degenerate elliptic operators under a vertical boundary condition forcing gradient blow-up. We identify the precise regime in which the problem admits a solution on a ball. In this regime, we prove rigidity: every solution domain is a ball, and the solution is uniquely determined by an explicit radial profile.
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