An $L^p$-approach to singular linear parabolic equations with lower order terms

Angelo Favini; Alfredo Lorenzi; Hiroki Tanabe; Atsushi Yagi

doi:10.3934/dcds.2008.22.989

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2008, Volume 22, Issue 4: 989-1008. Doi: 10.3934/dcds.2008.22.989

This issue Previous Article Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces Next Article The non-isothermal Allen-Cahn equation with dynamic boundary conditions

An $L^p$-approach to singular linear parabolic equations with lower order terms

1.
Università degli Studi di Bologn, Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40126 Bologna
2.
Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano
3.
Hirai Sanso 12-13, Takarazuka 665-0817
4.
Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871

Received: July 2007

Revised: October 2007

Published: October 2008

Abstract Related Papers Cited by

Abstract

Singular means here that the parabolic equation is neither in normal form nor can it be reduced to such a form. For this class of problems we generalizes the results proved in [4] introducing first-order terms.

Keywords:

Linear singular integro-differential equations of parabolic type Existence and uniqueness results. Spectral analysis of linear elliptic operators.

Mathematics Subject Classification: Primary: 35K20. Secondary 35K65, 35J25, 35P05.

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