Schroedinger and elliptic operators with distributional coefficients on a bounded domain

Details Schroedinger and elliptic operators with distributional coefficients on a bounded domain Schroedinger and elliptic operators with distributional coefficients on a bounded domain

2003-01-13

arxiv.org/abs/math/0301127v1

Mathematics

Functional Analysis

16 pages

Scientific paper

We study the operator $L=-\Delta+q$ on a bounded domain $\Omega\subset\mathbb R^n$, where $q(x)$ is a distributional potential. We find sufficient conditions for $q(x)$ which guarantee that $L$ is well--defined with Dirichlet and generalized Neumann boundary conditions. The asymptotics of the eigenvalues and the basis properties of the eigen- and associated functions of such operators are studied. The results are generalized for strongly elliptic operator of order $2m$ with Dirichlet boundary conditions.

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