Capillary Schwarz symmetrization in the half-space

Abstract

In this article, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a special anisotropic gauge, which enables us to transform the capillary symmetrization to the convex symmetrization introduced in Alvino et al. https:/doi.org/10.1016/S0294-1449(97)80147-3.

Keywords

• symmetrization
• capillary problem
• isoperimetric inequality
• anisotropic equations
• 35j25
• 35j65
• 49q20