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


Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.3103/S1055134416040027

Ключевые слова: elliptic operators, mixed problems, noncoercive boundary conditions, root functions, weighted Sobolev spaces

Аннотация: 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 surfaceПоказать полностью. 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. © 2016, Allerton Press, Inc.

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Журнал: Siberian Advances in Mathematics

Выпуск журнала: Vol. 26, Is. 4

Номера страниц: 247-293


  • Shlapunov A.A. (Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russian Federation)
  • Tarkhanov N.N. (Institut f?r Mathematik, Universit?t Potsdam, Potsdam, Germany)

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