Extending Sobolev functions with partially vanishing traces from locally -domains and applications to mixed boundary problems

详细信息    查看全文

• 作者：Kevin Brewster^a ; ^{kjb886@mail.mizzou.edu" class="auth_mail} ; Dorina Mitrea^a ; ¹ ; ^{mitread@missouri.edu" class="auth_mail} ; Irina Mitrea^b ; ² ; ^{imitrea@temple.edu" class="auth_mail} ; Marius Mitrea^a ; ³ ; ^{mitream@missouri.edu" class="auth_mail}
• 关键词：Higher-order Sobolev space ; Linear extension operator ; Locally (蔚 ; 未)(蔚 ; 未)-domain ; Higher-order boundary trace operator ; Real and complex interpolation ; Besov and Triebel&ndash ; Lizorkin spaces ; Bessel potential space and capacity ; Ahlfors regular set ; Synthesis ; Mixed boundary value problem ; Higher-order elliptic system
• 刊名：Journal of Functional Analysis
• 出版年：1 April, 2014
• 年：2014
• 卷：266
• 期：7
• 页码：4314-4421
• 全文大小：1135 K

文摘

We prove that given any , for each open set and any closed subset D of such that 惟 is locally an -domain near , there exists a linear and bounded extension operator mapping, for each , the space into . Here, with denoting either 惟 or , the space is defined as the completion in the classical Sobolev space of (restrictions to of) functions from whose supports are disjoint from D. In turn, this result is used to develop a functional analytic theory for the class (including intrinsic characterizations, boundary traces and extensions results, interpolation theorems, among other things) which is then employed in the treatment of mixed boundary value problems formulated in locally -domains. Finally, we also prove extension results on the scales of Besov and Bessel potential spaces on -domains with partially vanishing traces on Ahlfors regular sets and explore some of the implications of such extension results.