Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908851352109056 |
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| author | Bravin, Marco Gnann, Manuel V. Knüpfer, Hans Masmoudi, Nader Roodenburg, Floris B. Sauer, Jonas |
| author_facet | Bravin, Marco Gnann, Manuel V. Knüpfer, Hans Masmoudi, Nader Roodenburg, Floris B. Sauer, Jonas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge Bravin, Marco Gnann, Manuel V. Knüpfer, Hans Masmoudi, Nader Roodenburg, Floris B. Sauer, Jonas Analysis of PDEs 35J25, 35K05, 35B34, 35K67 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. |
| title | Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge |
| topic | Analysis of PDEs 35J25, 35K05, 35B34, 35K67 |
| url | https://arxiv.org/abs/2411.04651 |