---
res:
bibo_abstract:
- Let M be a complete Riemannian manifold of dimension d > 1, let P be a measure
on M with density exp U with respect to the Riemannian volume, and let Lf = Deltaf
+ **, where U is an element of H-loc(p,1)(M) and b = delU. It is shown
that in the case p > d and q is an element of [p', p] the operator L on the domain
C-0(infinity)(M) has a unique extension generating a C-0-semigroup on L-q(M, mu),
that is, the set (Z - I)(C-0(infinity)(M)) is dense in L-q(M, mu). In particular,
the operator L is essentially self-adjoint on L-2(M, mu). A similar result is
proved for elliptic operators with non-constant second order part that are formally
symmetric with respect to some measure.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Vladimir I.
foaf_name: Bogachev, Vladimir I.
foaf_surname: Bogachev
- foaf_Person:
foaf_givenName: Michael
foaf_name: Röckner, Michael
foaf_surname: Röckner
foaf_workInfoHomepage: http://www.librecat.org/personId=10585
bibo_doi: 10.1070/SM2003v194n07ABEH000750
bibo_issue: 7-8
bibo_volume: 194
dct_date: 2003^xs_gYear
dct_identifier:
- UT:000186261600002
dct_isPartOf:
- http://id.crossref.org/issn/1064-5616
dct_language: eng
dct_publisher: LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES@
dct_title: On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds@
...
**