Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains

Details Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains

2009-07-10

arxiv.org/abs/0907.1750v3

Mathematics

Analysis of PDEs

70 pages

Scientific paper

This paper has two main goals. First, we are concerned with the classification of self-adjoint extensions of the Laplacian $-\Delta\big|_{C^\infty_0(\Omega)}$ in $L^2(\Omega; d^n x)$. Here, the domain $\Omega$ belongs to a subclass of bounded Lipschitz domains (which we term quasi-convex domains), which contain all convex domains, as well as all domains of class $C^{1,r}$, for $r\in(1/2,1)$. Second, we establish Krein-type formulas for the resolvents of the various self-adjoint extensions of the Laplacian in quasi-convex domains and study the properties of the corresponding Weyl--Titchmarsh operators (or energy-dependent Dirichlet-to-Neumann maps). One significant technical innovation in this paper is an extension of the classical boundary trace theory for functions in spaces which lack Sobolev regularity in a traditional sense, but are suitably adapted to the Laplacian.

Affiliated with

Also associated with

No associations

Rating

Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas in Nonsmooth Domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-164362