Elliptic regularity and essential self-adjointness of Dirichlet operators on R^n (1996)
by
Vladimir I. Bogachev
,
Nicolai V. Krylov
,
Michael Röckner
| Citations: | 16 - 7 self |
BibTeX
@MISC{Bogachev96ellipticregularity,
author = {Vladimir I. Bogachev and Nicolai V. Krylov and Michael Röckner},
title = {Elliptic regularity and essential self-adjointness of Dirichlet operators on R^n},
year = {1996}
}
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Abstract
We prove a new regularity result for operators of type L = \Delta +B\Deltar+c, on open sets\Omega ae IR n , provided B :\Omega ! IR n , c :\Omega ! IR satisfy mild integrability conditions. As a consequence we prove that L = \Delta + r log ae \Delta r with domain C 1 0 (IR n ) is essentially self-adjoint on L 2 (IR n ; aedx), if ae 2 H 1;1 loc (IR n ) and r log ae 2 L fl loc (IR n ; dx) for some fl ? n.
