Approximation of elliptic and parabolic equations with Dirichlet boundary conditions

Abstract

We obtain an approximation result of the weak solutions to elliptic and parabolic equations with Dirichlet boundary conditions. We show that the weak solution can be obtained with a limit of approximations by regularizing the nonlinearities and approximating the domains.

Keywords

• nonlinear elliptic equations
• nonlinear parabolic equations
• approximations