Electron. J. Differential Equations, Vol. 2018 (2018), No. 45, pp. 1-23.

Nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity

Hocine Ayadi, Fares Mokhtari

In this article, we prove the existence and the regularity of distributional solutions for a class of nonlinear anisotropic elliptic equations with $p_i(x)$ growth conditions, degenerate coercivity and $L^{m(\cdot)}$ data, with $m(\cdot)$ being small, in appropriate Lebesgue-Sobolev spaces with variable exponents. The obtained results extend some existing ones [8,10].

Submitted May 18, 2017. Published February 12, 2018.
Math Subject Classifications: 35J70, 35J60, 35B65.
Key Words: Anisotropic elliptic equations; variable exponents; degenerate coercivity; distributional solutions; irregular data

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Hocine Ayadi
Département de mathématiques
Université Mohamed Boudiaf-M'sila
BP 166 M'sila 28000, Algeria
email: ayadi.hocine@yahoo.fr
Fares Mokhtari
Département de Mathématiques et Informatique
Université Benyoucef Benkhedda
Alger 1, 2 Rue Didouche Mourad, Algeria
email: fares_maths@yahoo.fr

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