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Well-posedness and regularity of the heat equation with Robin boundary conditions in the two-dimensional wedge

Journal Article (2025)
Author(s)

Marco Bravin (TU Delft - Electrical Engineering, Mathematics and Computer Science, Universidad de Cantabria)

Manuel V. Gnann (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Hans Knüpfer (Universität Heidelberg)

Nader Masmoudi (Courant Institute of Mathematical Sciences)

Floris B. Roodenburg (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Jonas Sauer (TU Delft - Electrical Engineering, Mathematics and Computer Science, Friedrich Schiller University Jena)

Research Group
Mathematical Physics
DOI related publication
https://doi.org/10.1080/03605302.2025.2534368 Final published version
More Info
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Publication Year
2025
Language
English
Research Group
Mathematical Physics
Journal title
Communications in Partial Differential Equations
Issue number
9
Volume number
50
Pages (from-to)
1099-1134
Downloads counter
187
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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.