Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge

Abstract

Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an $L^2$-setting of monomially weighted spaces. A mathematical framework is developed which allows to obtain arbitrarily high regularity without a smallness assumption on the opening angle of the wedge. The challenging aspect is that the resolvent problem exhibits two breakings of the scaling invariance, one in the equation and one in the boundary condition.

Typos fixed. Slight improvement of presentation, in particular a new overview over Chapter 3

References in corpus (2)

• Classical solutions to the thin-film equation with general mobility in the perfect-wetting regime
• Sobolev spaces with mixed weights and the Poisson equation on angular domains