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

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 smallnes...

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Bibliographic Details
Main Authors: Bravin, Marco (Author) , Gnann, Manuel V. (Author) , Knüpfer, Hans (Author) , Masmoudi, Nader (Author) , Roodenburg, Floris B. (Author) , Sauer, Jonas (Author)
Format: Article (Journal)
Language:English
Published: 04 August 2025
In: Communications in partial differential equations
Year: 2025, Volume: 50, Issue: 9, Pages: 1099-1134
ISSN:1532-4133
DOI:10.1080/03605302.2025.2534368
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1080/03605302.2025.2534368
Verlag, kostenfrei, Volltext: https://www.tandfonline.com/doi/full/10.1080/03605302.2025.2534368
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Author Notes:Marco Bravin, Manuel V. Gnann, Hans Knüpfer, Nader Masmoudi, Floris B. Roodenburg, and Jonas Sauer
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Summary: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.
Item Description:Gesehen am 08.12.2025
Physical Description:Online Resource
ISSN:1532-4133
DOI:10.1080/03605302.2025.2534368

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