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Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

Published online by Cambridge University Press:  10 December 2014

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)

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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