Title

WEIGHTED HARDY-RELLICH TYPE INEQUALITIES: IMPROVED BEST CONSTANTS AND SYMMETRY BREAKING.

Authors

CAZACU, CRISTIAN; FIDEL, IRINA

Abstract

When studying the weighted Hardy-Rellich inequality in L² 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.

Subjects

SPHERICAL harmonics; SYMMETRY breaking

Publication

Romanian Journal of Pure & Applied Mathematics / Revue Roumaine de Mathematiques Pures et Appliquees, 2024, Vol 69, Issue 3/4, p397

ISSN

0035-3965

Publication type

Academic Journal

DOI

10.59277/RRMPA.2024.397.413