The Dirichlet problem for nonlinear elliptic equations with variable exponent
Azeddine Baalal, Mohamed Berghout · Journal of Applied Analysis & Computation · 2019
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 $.