Weighted Hardy-Rellich type inequalities: improved best constants and symmetry breaking
Analysis of PDEs
2024-06-25 v1
Abstract
When studying the weighted Hardy-Rellich inequality in with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new sharp constant and to show that for some part of the weights is strictly larger than before. In some cases we emphasize that the extremals functions of the sharp constant are not radially symmetric.
Keywords
Cite
@article{arxiv.2406.15792,
title = {Weighted Hardy-Rellich type inequalities: improved best constants and symmetry breaking},
author = {Cristian Cazacu and Irina Fidel},
journal= {arXiv preprint arXiv:2406.15792},
year = {2024}
}