On L^p-resolvent estimates for second-order elliptic equations with lower order terms
- 발행기관 서강대학교 일반대학원
- 지도교수 김현석
- 발행년도 2017
- 학위수여년월 2017. 8
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000062136
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
We consider the Dirichlet and Neumann problems for second-order linear elliptic equations in divergence form. The leading coefficient $A$ has small BMO semi-norm and first-order coefficient $b$ belongs to $L^r$, where $n \leq r < \infty$ if $n \geq 3$ and $2 < r < \infty$ if $n=2$. We first establish $L^p$-resolvent estimates for Dirichlet problems on bounded domains having small Lipschitz constant when $r/(r-1) < p < \infty$. Under the additional assumption $\mbox{div} \, A \in L^r$, we also establish $L^p$-resolvent estimates on bounded domains with $C^{1,1}$ boundary when $1 < p < r$. Moreover, we next prove $L^p$-resolvent estimates for Neumann problems on bounded domains having small Lipschitz constant when $r/(r-1) < p < \infty$. These results allow us to show that the operators corresponding our elliptic equations generate analytic semigroups in $L^p(\Omega)$.
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