Generalized Polya-Szego inequality and applications to some quasi-linear elliptic problems

Abstract

We generalize Polya-Szego inequality to integrands depending on $u$ and its gradient. Under minimal additional assumptions, we establish equality cases in this generalized inequality. We also give relevant applications of our study to a class of quasi-linear elliptic equations and systems.

21 pages

References in corpus (3)

• Explicit approximation of the symmetric rearrangement by polarizations
• On the symmetry of minimizers
• Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations

Cited by in corpus (4)

• A weak-strong convergence property and symmetry of minimizers of constrained variational problems in ${\mathbb{R}}^N$
• On Symmetry of Minimizers in Constrained Quasi-Linear Problems, 1
• Stability and instability results for standing waves of quasi-linear Schrödinger equations
• Radial symmetry of minimax critical points for nonsmooth functionals