Open AccessNondivergence parabolic equations in weighted variable exponent spaces
Author(s) -
SunSig Byun,
Mikyoung Lee,
Jihoon Ok
Publication year - 2017
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7352
Subject(s) - exponent , mathematics , domain (mathematical analysis) , algorithm , mathematical analysis , philosophy , linguistics
We prove the global Calderón-Zygmund estimates for second order parabolic equations in nondivergence form in weighted variable exponent Lebesgue spaces. We assume that the associated variable exponent is log-Hölder continuous, the weight is of a certain Muckenhoupt class with respect to the variable exponent, the coefficients of the equation are the functions of small bonded mean oscillation, and the underlying domain is a C 1 , 1 C^{1,1} -domain.