DOI: 10.1515/acv-2025-0109 ISSN: 1864-8258

Overdetermined fractional Serrin problem

Nicola Garofalo, Dimiter Vassilev
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Abstract

In this work, we establish a Serrin-type symmetry result for a class of degenerate elliptic operators that naturally arise in the theory of generalized axially symmetric potentials. The relevant differential operator is

L a = ∂ r ⁢ r ⁡ u + a r ⁢ ∂ r ⁡ u + Δ y ⁢ u {L_{a}=\partial_{rr}u+\frac{a}{r}\partial_{r}u+\Delta_{y}u}
, where
a ≥ 0 {a\geq 0}
represents the fractional parameter.

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