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Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

Part of: Harmonic analysis in several variables Miscellaneous topics - Partial differential equations Special classes of linear operators Representations of solutions Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  10 December 2014

Vagif S. Guliyev  and
Lubomira G. Softova
Vagif S. Guliyev
Affiliation:
Department of Mathematics, Ahi Evran University, Kirsehir, Turkey Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan, (vagif@guliyev.com)
Lubomira G. Softova
Affiliation:
Department of Civil Engineering, Design, Construction Industry and Environment, Second University of Naples, Via Roma 29, Aversa (CE) 81031, Italy, (luba.softova@unina2.it)
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Abstract

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We prove continuity in generalized parabolic Morrey spaces of sublinear operators generated by the parabolic Calderón—Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. As a consequence, we obtain a global -regularity result for the Cauchy—Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation (VMO) coefficients.

Keywords

generalized Morrey spacessublinear operatorsCalderón—Zygmund integralsBMOVMOCauchy—Dirichlet problem

MSC classification

Primary: 35K20: Initial-boundary value problems for second-order parabolic equations
Secondary: 35B45: A priori estimates 35D35: Strong solutions 35R05: Partial differential equations with discontinuous coefficients or data 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 47B38: Operators on function spaces (general)

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 199 - 218
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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