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arXiv · 2607.18952

Serrin problems with vertical boundary behavior

Julián Pozuelo·Simone Verzellesi
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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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Julián Pozuelo, Simone Verzellesi. 2026-07-21. Serrin problems with vertical boundary behavior. https://arxiv.org/abs/2607.18952

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