A basis of resolutive sets for the heat equation: an elementary construction

Authors

  • Alessia E. Kogoj Università di Urbino
  • Ermanno Lanconelli Università di Bologna

DOI:

https://doi.org/10.6092/issn.2240-2829/16154

Keywords:

Heat equation, caloric Dirichlet problem, Perron solution, Potential Analysis

Abstract

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.

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Published

2023-01-09

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