Shape of extremal functions for weighted Sobolev-type inequalities

2023/11/02 by Brock, Friedemann, Chiacchio, Francesco, Croce, Gisella +1
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2311.01083

Abstract

We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem.

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