TY - JOUR
AB - 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.
AU - Bogachev, Vladimir I.
AU - Röckner, Michael
ID - 1609835
IS - 7-8
JF - Sbornik: Mathematics
SN - 1064-5616
TI - On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds
VL - 194
ER -
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