Well-posedness and regularity of the heat equation with Robin boundary conditions in the two-dimensional wedge
Marco Bravin (TU Delft - Analysis, University of Cantabria)
Manuel V. Gnann (TU Delft - Mathematical Physics)
H. Knüpfer (University of Heidelberg)
Nader Masmoudi (Courant Institute of Mathematical Sciences)
F.B. Roodenburg (TU Delft - Analysis)
Jonas Sauer (Friedrich Schiller University Jena, TU Delft - Analysis)
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Abstract
Abstract.: Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge are established in an L2-setting of monomially weighted spaces. A mathematical framework is developed that allows us 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.
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