A class of overdetermined problem for fractional Capacity

Abstract

In this paper, we consider an unconventional overdetermined problem through a property of concavity, which provides some characterizations of balls via Brunn-Minkowski inequalities. In this setting, our rsults can be viewed as the generalization of $p$-capacity in [14], which have its own interest.

This article was written in the summer of 2023, and still under review. All comments are welcome