Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. I
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  • 作者：A. A. Shlapunov ; N. Tarkhanov
  • 关键词：mixed problem ; noncoercive boundary condition ; elliptic operator ; root function ; weighted Sobolev space
  • 刊名：Siberian Advances in Mathematics
  • 出版年：2016
  • 出版时间：January 2016
  • 年：2016
  • 卷：26
  • 期：1
  • 页码：30-76
  • 全文大小：1,154 KB
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  • 作者单位：A. A. Shlapunov (1)
    N. Tarkhanov (2)

    1. Siberian Federal University, Krasnoyarsk, 660041, Russia
    2. Universität Potsdam, Potsdam, 14469, Germany
  • 刊物类别：Mathematics and Statistics
  • 刊物主题：Mathematics
    Mathematics
    Russian Library of Science
  • 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
  • ISSN：1934-8126
文摘
We consider (in general noncoercive) mixed problems in a bounded domain D in ℝ n for a second-order elliptic partial differential operator A(x, Ə). It is assumed that the operator is written in divergent form in D, the boundary operator B(x, Ə) is the restriction of a linear combination of the function and its derivatives to ƏD and the boundary of D is a Lipschitz surface. We separate a closed set Y ⊂ ƏD 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, where the weight is a power of the distance to the singular set Y. Finally, we prove the completeness of the root functions associated with L.
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