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arXiv · 2311.01083

Shape of extremal functions for weighted Sobolev-type inequalities

Friedemann Brock·Francesco Chiacchio·Gisella Croce·Anna Mercaldo
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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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Friedemann Brock, Francesco Chiacchio, Gisella Croce, Anna Mercaldo. 2023-11-02. Shape of extremal functions for weighted Sobolev-type inequalities. https://arxiv.org/abs/2311.01083

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