A mapping property of the heat volume potential

Paolo Luzzini

doi:10.1007/s40574-023-00383-7

A mapping property of the heat volume potential

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of Hölder continuous functions. As an application we solve the Dirichlet and Neumann problems for the heat equation with a non-homogeneous term in such space of distributions.

Lingua originale	Inglese
pagine (da-a)	401-416
Numero di pagine	16
Rivista	Bolletino dell Unione Matematica Italiana
Volume	17
Numero di pubblicazione	2
DOI	https://doi.org/10.1007/s40574-023-00383-7
Stato di pubblicazione	Pubblicato - giu 2024
Pubblicato esternamente	Sì

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10.1007/s40574-023-00383-7

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abstract = "We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H{\"o}lder continuous functions. As an application we solve the Dirichlet and Neumann problems for the heat equation with a non-homogeneous term in such space of distributions.",

keywords = "31B10, 35K05, 35K20, 47G10, Heat equation, Initial-boundary value problems, Regularity theory for integral operators, Volume potential",

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A mapping property of the heat volume potential

Abstract

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