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The Dirichlet problem for nonlinear elliptic equations with variable exponent |
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| Authors: | Azeddine Baalal and Mohamed Berghout |
| Institution: | Department of Mathematics, Faculty of Sciences A\"{\i}n Chock, University Hassan II Casablanca B.P. 5366 M\^{a}arif, Casablanca, Morocco and Department of Mathematics, Faculty of Sciences A\"{\i}n Chock, University Hassan II Casablanca B.P. 5366 M\^{a}arif, Casablanca, Morocco |
| 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 $g$. |
| Keywords: | p( )-Laplacian operator potential theory Sobolev spaces with variable exponent |
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