Nonlinear anisotropic elliptic equations in
with variable exponents and locally integrable data |
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| Authors: | Fares Mokhtari |
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| Affiliation: | 1. Department of Mathematics, University of Benyoucef Benkhedda (Alger 1), and Laboratory of NLPDE ENS‐Kouba, Algiers, Algeria;2. Department of Mathematics, Faculty of Sciences, University of Benyoucef Benkhedda (Alger 1), Algiers, Algeria |
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| Abstract: | 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 whole  with 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. |
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| Keywords: | nonlinear elliptic equations variable exponents anisotropic equations Lloc1‐ data |
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with 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.