Partial regularity for flows of H-surfaces

Abstract

This article studies regularity of weak solutions to the heat equation for H-surfaces. Under the assumption that the function H is Lipschitz and depends only on the first two components, the solution has regularity on its domain, except for a set of measure zero. Moreover, if the solution satisfies certain energy inequality, this set is finite.

Keywords

• H-surfaces
• Hardy spaces
• Lorentz spaces.