Capillary Schwarz symmetrization in the half-space

Abstract

In this paper, 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 \cite{AFT97}.

arXiv comment15 pages

References in corpus (4)

• Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities
• Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
• Heintze-Karcher inequality and capillary hypersurfaces in a wedge

Cited by in corpus (4)

• Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains
• Stability of the Wulff shape with respect to anisotropic curvature functionals
• Half-space Liouville-type theorems for minimal graphs with capillary boundary
• Willmore-type inequality in unbounded convex sets