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The Dirichlet Problem for Nonlinear Elliptic Equations with Variable Exponent
Mohamed BERGHOUT,Azeddine Baalal
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.