Sturm–Liouville problems in weighted spaces in domains with non-smooth edges. II

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• 作者：A. A. Shlapunov ; N. N. Tarkhanov
• 关键词：mixed problems ; noncoercive boundary conditions ; elliptic operators ; root functions ; weighted Sobolev spaces
• 刊名：Siberian Advances in Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：26
• 期：4
• 页码：247-293
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Allerton Press
• ISSN：1934-8126
• 卷排序：26

文摘

We consider a (generally, noncoercive) mixed boundary value problem in a bounded domain D of Rn for a second order elliptic differential operator A(x, ∂). The differential operator is assumed to be of divergent form in D and the boundary operator B(x, ∂) is of Robin type on ∂D. The boundary of D is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset Y ⊂ ∂D and control the growth of solutions near Y. We prove that the pair (A, B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set Y. Moreover, we prove the completeness of root functions related to L.