Existence of &i&T&/i&-&i&ν&/i&-&i&p&/i&(&i&x&/i&)-Solution of a Nonhomogeneous Elliptic Problem with Right Hand Side Measure

摘要

Using the theory of weighted Sobolev spaces with variable exponent and the L ~(1)-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.