A mapping property of the heat volume potential
type: Item
instance of: scholarly article
title: A mapping property of the heat volume potential
zbMATH Open document ID: 1548.35151
author: Paolo Luzzini
published in: Bollettino dell'Unione Matematica Italiana
publication date: 2024-07-01T00:00:00Z
review text: The paper under review deals with mapping properties of the volume potential for the heat equation in anisotropic Hölder spaces. More precisely, the author considers the heat volume potential \(P[f]\) associated to a function \(f\) in the parabolic cylinder \(\Omega_T=\overline{]-\infty,T[}\times \Omega\) and prove that \(P[\cdot]\) is a bounded linear operator from \(C^{\frac{-1+\alpha}{2};\beta}(\overline{\Omega_T})\) to \(C^{\frac{1+\alpha}{2};1+\alpha}(\overline{\Omega_T})\). Then the author applies the obtained results to Dirichlet and Neumann problems for the equation\N\[\N\partial_t u-\Delta u=\partial_t f\, .\N\]
reviewed by: Paolo Musolino
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 7873919
zbMATH Keywords: heat equation
zbMATH Keywords: volume potential
zbMATH Keywords: regularity theory for integral operators
zbMATH Keywords: initial-boundary value problems
MaRDI profile type: Publication
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DOI: 10.1007/S40574-023-00383-7
description: scientific article; zbMATH DE number 7873919