The Dirichlet problem for elliptic equations with Lp,q-data
- 주제어 (키워드) Elliptic equations , Dirichlet Problem , Real interpolation , Sobolev-Lorentz spaces
- 발행기관 서강대학교 일반대학원
- 지도교수 김현석
- 발행년도 2022
- 학위수여년월 2022. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제 URI http://www.dcollection.net/handler/sogang/000000066469
- UCI I804:11029-000000066469
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권 보호를 받습니다.
초록 (요약문)
In this thesis, we consider the Dirichlet problem for elliptic equations with data in Lorentz spaces L^{p,q} on bounded W^{2,n,1}-domains. First, we establish the solvability of the Poisson equation for the cases 1<p<n, 1≤q≤∞ and p=n,q=1. Then, under certain conditions on coefficients, we obtain the solvability of Lu=-a^{ij}D_{ij}u+b^{i}D_{i}u+cu=f with L^{p,q}-data. By using a duality argument, we also obtain the existence and uniqueness of very weak solutions of L^{*}v=-D_{ij}(a^{ij}v)-D_{i}(b^{i}v)+cv=div g, where g∈L^1(Ω;R^n).
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