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Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

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

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, ([email protected])
Lubomira G. Softova
Affiliation:
Department of Civil Engineering, Design, Construction Industry and Environment, Second University of Naples, Via Roma 29, Aversa (CE) 81031, Italy, ([email protected])
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Abstract

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)
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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