Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 67-83

GLOBAL GRADIENT ESTIMATES IN WEIGHTED LEBESGUE SPACES FOR PARABOLIC OPERATORS

Sun-Sig Byun, Dian K. Palagachev and Lubomira G. Softova

Seoul National University, Department of Mathematical Sciences and Research Institute of Mathematics
Seoul 151-747, Korea; byun 'at' snu.ac.kr

Politecnico di Bari, Dipartimento di Meccanica, Matematica e Management (DMMM)
Via E. Orabona 4, 70125 Bari, Italy; dian.palagachev 'at' poliba.it

Second University of Naples, Department of Civil Engineering, Design, Construction Industry and Environment
Via Roma 29, 81031 Aversa, Italy; luba.softova 'at' unina2.it

Abstract. We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and in the mechanics of membranes and films of simple non-homogeneous materials which form a linear laminated medium. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderón-Zygmund type theory for such parabolic operators in the settings of the weighted Lebesgue spaces. As consequence of the main result, we get regularity in parabolic Morrey scales for the spatial gradient of the weak solutions to the problems considered.

2010 Mathematics Subject Classification: Primary 35K20; Secondary 35R05, 35B65, 35B45, 46E30, 35K40, 42B25, 74E30.

Key words: Weighted Lebesgue space, Muckenhoupt weight, parabolic system, Cauchy-Dirichlet problem, measurable coefficients, BMO, gradient estimates, Morrey space, linear laminates.

Reference to this article: S.-S. Byun, D. K. Palagachev and L. G. Softova: Global gradient estimates in weighted Lebesgue spaces for parabolic operators. Ann. Acad. Sci. Fenn. Math. 41 (2016), 67-83.

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doi:10.5186/aasfm.2016.4102