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Research Article | Open Access

Approximation of elliptic and parabolic equations with Dirichlet boundary conditions

Youchan Kim1( ), Seungjin Ryu1, Pilsoo Shin2
Department of Mathematics, University of Seoul, 163 Seoulsiripdaero, Dongdaemun-gu, Seoul 02504, Republic of Korea
Department of Mathematics, Kyonggi University, 154-42 Gwanggyosan-ro, Yeongtong-gu, Suwon 16227, Republic of Korea
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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 equationsnonlinear parabolic equationsapproximations

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Mathematics in Engineering
Volume 5 Issue 4,
August 2023
Pages 1-43
DOI: 10.3934/mine.2023079

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Cite this article:
Kim Y, Ryu S, Shin P. Approximation of elliptic and parabolic equations with Dirichlet boundary conditions. Mathematics in Engineering, 2023, 5(4): 1-43. https://doi.org/10.3934/mine.2023079

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Received: 22 August 2022
Revised: 08 January 2023
Accepted: 08 March 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)