@article{Kim2023, 
author = {Youchan Kim and Seungjin Ryu and Pilsoo Shin},
title = {Approximation of elliptic and parabolic equations with Dirichlet boundary conditions},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {4},
pages = {1-43},
keywords = {nonlinear elliptic equations, nonlinear parabolic equations, approximations},
url = {https://www.sciopen.com/article/10.3934/mine.2023079},
doi = {10.3934/mine.2023079},
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.}
}