Conditional stability for backward parabolic equations with LogLipt×Lipx-coefficients. (July 2015)

• Record Type: Journal Article
• Authors: Del Santo, Daniele; Jäh, Christian P.; Prizzi, Martino
• Is Part Of: Nonlinear analysis. Volume 121(2015)
• Page Start: 101
• Page End: 122
• Publication Date: 2015-07
• Subjects: 35B30 -- 34A12 -- 35A02; Conditional stability -- Backward-parabolic equation -- Low regularity coefficients -- Weighted energy estimate -- Bony's paraproduct; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work we present an improvement of Del Santo and Prizzi (2009), where the authors proved a result concerning continuous dependence for backward-parabolic operators whose coefficients are Log-Lipschitz in t and C 2 in x . In that paper, the C 2 regularity with respect to x had to be assumed for technical reasons: here we remove this assumption, replacing it with Lipschitz-continuity. The main tools in the proof are Littlewood–Paley theory and Bony's paraproduct.