Fractional powers of operators corresponding to coercive problems in Lipschitz domains
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- 作者：M. S. Agranovich (113)
A. M. Selitskii (213) - 关键词：Lipschitz domain ; strongly elliptic system ; coercive problem ; Kato’s square root problem
- 刊名：Functional Analysis and Its Applications
- 出版年：2013
- 出版时间：April 2013
- 年：2013
- 卷：47
- 期：2
- 页码：83-95
- 全文大小：215KB
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A. M. Selitskii (213)
113. National Research University Higher School of Economics, Moscow, Russia
213. Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, Russia
文摘
Let Ω be a bounded Lipschitz domain in ?sup class="a-plus-plus"> n , n ?2, and let L be a second-order matrix strongly elliptic operator in Ω written in divergence form. There is a vast literature dealing with the study of domains of fractional powers of operators corresponding to various problems (beginning with the Dirichlet and Neumann problems) with homogeneous boundary conditions for the equation Lu = f, including the solution of the Kato square root problem, which arose in 1961. Mixed problems and a class of problems for higher-order systems have been covered as well. We suggest a new abstract approach to the topic, which permits one to obtain the results that we deem to be most important in a much simpler and unified way and cover new operators, namely, classical boundary operators on the Lipschitz boundary Γ = ?/em>Ω or part of it. To this end, we simultaneously consider two well-known operators associated with the boundary value problem.