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Volume 9, Number 1, 2019, Pages 295-313                                                                DOI:10.11948/2019.295
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 $g$.
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