Mixed type boundary value problem of elliptic equation in a thin domain

Fuente: arXiv
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Main Authors: Hu, Dian, Huang, Genggeng
Format: Preprint
Published: 2024
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author Hu, Dian
Huang, Genggeng
author_facet Hu, Dian
Huang, Genggeng
contents In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while the other part of the boundary is subject to a Dirichlet boundary condition. We show that, as the crescent-shaped area collapses into a segment under suitable conditions, the boundary value problem obeys uniform Schauder estimates and induces an asymptotic estimate.
format Preprint
id arxiv_https___arxiv_org_abs_2407_03592
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Mixed type boundary value problem of elliptic equation in a thin domain
Hu, Dian
Huang, Genggeng
Analysis of PDEs
In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while the other part of the boundary is subject to a Dirichlet boundary condition. We show that, as the crescent-shaped area collapses into a segment under suitable conditions, the boundary value problem obeys uniform Schauder estimates and induces an asymptotic estimate.
title Mixed type boundary value problem of elliptic equation in a thin domain
topic Analysis of PDEs
url https://arxiv.org/abs/2407.03592