The Dirichlet problem for nonlinear elliptic equations with variable exponent

Azeddine Baalal; Mohamed Berghout

doi:10.11948/2019.295

2019 Volume 9 Issue 1

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Azeddine Baalal, Mohamed Berghout. The Dirichlet problem for nonlinear elliptic equations with variable exponent[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 295-313. doi: 10.11948/2019.295

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Azeddine Baalal, Mohamed Berghout. The Dirichlet problem for nonlinear elliptic equations with variable exponent[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 295-313. doi: 10.11948/2019.295

The Dirichlet problem for nonlinear elliptic equations with variable exponent

Department of Mathematics, Faculty of Sciences Aùn Chock, University Hassan II Casablanca B.P. 5366 Mâarif, Casablanca, Morocco

Corresponding author: Email address:moh.berghout@gmail.com(M. Berghout)

Abstract

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 $.
- $ p(.)$-Laplacian operator /
- potential theory /
- Sobolev spaces with variable exponent
MSC: 35B30, 31C05, 46E35

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References

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