TITLE:
Existence of T-ν-p(x)-Solution of a Nonhomogeneous Elliptic Problem with Right Hand Side Measure
AUTHORS:
El Houcine Rami, Abdelkrim Barbara, El Houssine Azroul
KEYWORDS:
Nonhomogeneous Elliptic Equations, Dirichlet Problems, Weighted Sobolev Spaces with Variable Exponent, Minty’s Lemma, T-ν-p(x)-Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.11,
November
15,
2021
ABSTRACT: Using the theory of weighted Sobolev spaces with variable exponent and the L1-version on Minty’s lemma, we investigate the existence of solutions for some nonhomogeneous Dirichlet problems generated by the Leray-Lions operator of divergence form, with right-hand side measure. Among the interest of this article is the given of a very important approach to ensure the existence of a weak solution of this type of problem and of generalization to a system with the minimum of conditions.