Solvability in Lorentz spaces for Stokes equations
- 발행기관 서강대학교 일반대학원
- 지도교수 김현석
- 발행년도 2011
- 학위수여년월 2011. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000046587
- 저작권 서강대학교의 논문은 저작권 보호를 받습니다.
초록/요약
We consider the stationary Stokes equations in a bounded smooth domain $\Omega$ in $\textbf{R}^n$, $ n\geq 2$. For $1<p<\infty$ and $1\leq q \leq \infty$, we assume that the boundary data $g$ belongs to $W^{-1/p,p,q}(\partial\Omega)$ which is the dual space of $W^{1-1/p',p',q'}(\partial\Omega)$. We prove the existence and uniqueness of a very weak solution $v$ in the Lorentz space $L^{p,q}(\Omega)$. Here $W^{1-1/p',p',q'}(\partial\Omega)$ is defined as the trace space of the Sobolev-Lorentz space $W^{1,p',q'}(\Omega)$ by using the classical trace theorem and real interpolation method.
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