@article{1609835,
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.},
author = {Bogachev, Vladimir I. and Röckner, Michael},
issn = {1064-5616},
journal = {Sbornik: Mathematics},
number = {7-8},
pages = {969--978},
publisher = {LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES},
title = {{On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds}},
doi = {10.1070/SM2003v194n07ABEH000750},
volume = {194},
year = {2003},
}
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