On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds
Bogachev, Vladimir I.
Röckner, Michael
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 + <b, delf>, 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.
LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES
2003
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/1609835
Bogachev VI, Röckner M. On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. <em>Sbornik: Mathematics</em>. 2003;194(7-8):969-978.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1070/SM2003v194n07ABEH000750
info:eu-repo/semantics/altIdentifier/issn/1064-5616
info:eu-repo/semantics/altIdentifier/wos/000186261600002
info:eu-repo/semantics/closedAccess