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The heat equation with rough boundary conditions and holomorphic functional calculus

Lindemulder, N.; Veraar, M.

In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded H$^{∞}$-calculus on weighted L$^{p}$-spaces for power weights which fall outside the classical class of A$_{p}$-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with rough inhomogeneous boundary data.

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Verlagsausgabe §
DOI: 10.5445/IR/1000119489
Veröffentlicht am 04.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0022-0396, 1090-2732
KITopen-ID: 1000119489
Erschienen in Journal of differential equations
Verlag Elsevier
Band 269
Heft 7
Seiten 5832-5899
Vorab online veröffentlicht am 21.04.2020
Nachgewiesen in Scopus
Web of Science
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