On some nonlinear elliptic equations with measurable boundary conditions in anisotropic weighted Sobolev spaces

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Said Ait Dada Alla
Ouidad Azraibi
Badr El Haji

Abstract

The novelty of this paper is to establish an existence of entropy solutions for anisotropic elliptic equation looks like -div B(x, ν, ∇ ν)+H(x, ν)=f-div F where the datum f ∈ L1(Ω) and F ∈ ∏i=1N Lp′i(Ω, wi*) and H(x, ν) ∈ L1(Ω). Furthermore, only the large monotonicity conditions will be assumed on B(x, s, ξ). To overcome this difficulty, we will use the approach of Minty's lemma in the anisotropic weighted Sobolev spaces.

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How to Cite
Ait Dada Alla, S., Azraibi, O., & El Haji, B. (2024). On some nonlinear elliptic equations with measurable boundary conditions in anisotropic weighted Sobolev spaces. Gulf Journal of Mathematics, 17(1), 130-141. https://doi.org/10.56947/gjom.v17i1.1712
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