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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
Department of Mathematics, Ahi Evran University, Kirsehir, Turkey Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan, (
Lubomira G. Softova
Department of Civil Engineering, Design, Construction Industry and Environment, Second University of Naples, Via Roma 29, Aversa (CE) 81031, Italy, (


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.

Research Article
Copyright © Edinburgh Mathematical Society 2015 

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