Shape of extremal functions for weighted Sobolev-type inequalities
Optimization and Control
2025-07-22 v2
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.
Cite
@article{arxiv.2311.01083,
title = {Shape of extremal functions for weighted Sobolev-type inequalities},
author = {Friedemann Brock and Francesco Chiacchio and Gisella Croce and Anna Mercaldo},
journal= {arXiv preprint arXiv:2311.01083},
year = {2025}
}