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 tt 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.

Conditional stability for backward parabolic equations with LogLip_txLip_x-coefficients

DEL SANTO, DANIELE;PRIZZI, Martino
2015

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 tt 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.
http://www.sciencedirect.com/science/article/pii/S0362546X14004106#
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2830720
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