Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2015

Ключевые слова: mixed problems, non-coercive boundary conditions, parameter dependent elliptic operators, root functions

Аннотация: We consider a non-coercive mixed boundary value problem in a bounded domain D of R-n for a second order parameter-dependent elliptic differential operator A(x, partial derivative, lambda) with complex-valued essentially bounded measured coefficients and complex parameter lambda. The differential operator is assumed to be of divergent form in D, the boundary operator B(x, partial derivative) is of Robin type with possible pseudo-differential components on partial derivative D. The boundary of D is assumed to be a Lipschitz surface. Under these assumptions the pair (A (x, partial derivative, lambda), B) induces a holomorphic family of Fredholm operators L(lambda) : H+(D) --> H-(D) in suitable Hilbert spaces H+(D), H-(D) of Sobolev type. If the argument of the complex-valued multiplier of the parameter in A(x, partial derivative, lambda) is continuous, then we prove that the operators L(lambda) are continuously invertible for all lambda with sufficiently large modulus vertical bar lambda vertical bar on each ray on the complex plane C where the operator A(x, partial derivative, lambda) is parameter-dependent elliptic. We also describe reasonable conditions for the system of root functions related to the family L(lambda) to be (doubly) complete in the spaces H+(D), H-(D) and the Lebesgue space L-2(D).

Журнал: MATHEMATICAL COMMUNICATIONS

Выпуск журнала: Vol. 20, Is. 2

Номера страниц: 131-150

ISSN журнала: 13310623

Место издания: OSIJEK

Издатель: UNIV OSIJEK, DEPT MATHEMATICS

• Polkovnikov Alexander (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk 660011, Russia)
• Shlapunov Alexander (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk 660011, Russia)

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