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 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.
Authors
- Manuel V. Gnann (ORCID: https://orcid.org/0000-0002-1479-0387)
- Jonas Sauer (ORCID: https://orcid.org/0000-0001-8998-4517)
- Hans Knüpfer (ORCID: https://orcid.org/0000-0002-5861-772X)
- Nader Masmoudi (ORCID: https://orcid.org/0000-0002-8102-8130)
- Marco Bravin (ORCID: https://orcid.org/0000-0001-7366-5722)
- Floris B. Roodenburg
Institutions
- Heidelberg University (DE)
- Courant Institute of Mathematical Sciences (US)
- Brazilian Society of Computational and Applied Mathematics (BR)
- Jena University Hospital (DE)
- Heidelberg University (US)
- Delft University of Technology (NL)
Publication Details
- Journal
- Communications in Partial Differential Equations
- Published
- 2025-08-04
- DOI
- https://doi.org/10.1080/03605302.2025.2534368
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Deutsche Forschungsgemeinschaft
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Tamkeen