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

Marco Bravin; Manuel V. Gnann; Hans Knüpfer; Nader Masmoudi; Floris B. Roodenburg; Jonas Sauer

doi:10.1080/03605302.2025.2534368

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

Marco Bravin, Manuel V. Gnann, Hans Knüpfer, Nader Masmoudi, Floris B. Roodenburg, Jonas Sauer^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

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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.

Original language	English
Pages (from-to)	1099-1134
Number of pages	36
Journal	Communications in Partial Differential Equations
Volume	50
Issue number	9
DOIs	https://doi.org/10.1080/03605302.2025.2534368
Publication status	Published - 2025

Keywords

heat equation
higher regularity
non-smooth domain
Robin boundary conditions
unbounded domain

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10.1080/03605302.2025.2534368

Well-posedness and regularity of the heat equation with Robin boundary conditions in the two-dimensional wedgeFinal published version, 2.87 MBLicence: CC BY

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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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AU - Bravin, Marco

AU - Gnann, Manuel V.

AU - Knüpfer, Hans

AU - Masmoudi, Nader

AU - Roodenburg, Floris B.

AU - Sauer, Jonas

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - heat equation

KW - higher regularity

KW - non-smooth domain

KW - Robin boundary conditions

KW - unbounded domain

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DO - 10.1080/03605302.2025.2534368

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SP - 1099

EP - 1134

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 9

ER -

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

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Keywords

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