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Nonlinear anisotropic elliptic equations in R N with variable exponents and locally integrable data
Author(s) -
Mokhtari Fares
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4137
Subject(s) - sobolev space , mathematics , smoothness , sobolev inequality , integrable system , mathematical analysis , anisotropy , nonlinear system , lp space , critical exponent , variable (mathematics) , pure mathematics , lebesgue integration , compact space , banach space , geometry , physics , quantum mechanics , scaling
In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the wholeR Nwith variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd.