A basis of resolutive sets for the heat equation: an elementary construction
Keywords:Heat equation, caloric Dirichlet problem, Perron solution, Potential Analysis
By an easy “trick” taken from the caloric polynomial theory, we prove the existence of a basis of the Euclidean topology whose elements are resolutive sets of the heat equation. This result can be used to construct, with a very elementary approach, the Perron solution of the caloric Dirichlet problem on arbitrary bounded open subsets of the Euclidean space-time.
How to Cite
Kogoj, A. E., & Lanconelli, E. (2022). A basis of resolutive sets for the heat equation: an elementary construction. Bruno Pini Mathematical Analysis Seminar, 13(1), 1–8. https://doi.org/10.6092/issn.2240-2829/16154
Copyright (c) 2022 Alessia E. Kogoj, Ermanno Lanconelli
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