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
Citation: 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

  • 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 $.
    MSC: 35B30, 31C05, 46E35
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