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 Volume 9, Number 1, 2019, Pages 295-313 The Dirichlet problem for nonlinear elliptic equations with variable exponent Azeddine Baalal,Mohamed Berghout Keywords:p(.)-Laplacian operator, potential theory, Sobolev spaces with variable exponent. Abstract: In this paper we study the Dirichlet problem for nonlinear elliptic equations with variable exponents in Sobolev spaces with variable exponent. We show that for every continuous function $g$ on the boundary there exists a unique continuous extension of $g$. PDF      Download reader