On the Perron solution of the caloric Dirichlet problem: an elementary approach

On the Perron solution of the caloric Dirichlet problem: an elementary approach

By an easy trick taken from caloric polynomial theory, we construct a family B of almost regular domains for the caloric Dirichlet problem. B is a basis of the Euclidean topology. This allows to build, with a basically elementary procedure, the Perron solution to the caloric Dirichlet problem on eve...

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Veröffentlicht in:Journal of evolution equations 2022-06, Vol.22 (2), Article 43
Hauptverfasser: Kogoj, Alessia E., Lanconelli, Ermanno
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Dirichlet problem
Domains
Mathematics
Mathematics and Statistics
Polynomials
Topology
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Zusammenfassung:By an easy trick taken from caloric polynomial theory, we construct a family B of almost regular domains for the caloric Dirichlet problem. B is a basis of the Euclidean topology. This allows to build, with a basically elementary procedure, the Perron solution to the caloric Dirichlet problem on every bounded domain.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-022-00795-6