**, 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.","lang":"eng"}],"author":[{"last_name":"Bogachev","full_name":"Bogachev, Vladimir I.","first_name":"Vladimir I."},{"id":"10585","last_name":"Röckner","first_name":"Michael","full_name":"Röckner, Michael"}],"page":"969-978","department":[{"_id":"10020"}],"date_created":"2010-04-28T12:58:45Z","publication":"Sbornik: Mathematics","language":[{"iso":"eng"}],"year":"2003","type":"journal_article","article_type":"original","citation":{"frontiers":"Bogachev, V. I., and Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. ***Sbornik: Mathematics* 194, 969-978.","wels":"Bogachev, V. I.; Röckner, M. (2003): On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds *Sbornik: Mathematics*,194:(7-8): 969-978.","dgps":"Bogachev, V.I. & Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*, *194*(7-8), 969-978. LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES. doi:10.1070/SM2003v194n07ABEH000750.

","lncs":" Bogachev, V.I., Röckner, M.: On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. Sbornik: Mathematics. 194, 969-978 (2003).","harvard1":"Bogachev, V.I., & Röckner, M., 2003. On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*, 194(7-8), p 969-978.","angewandte-chemie":"V. I. Bogachev, and M. Röckner, “On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds”, *Sbornik: Mathematics*, **2003**, *194*, 969-978.","bio1":"Bogachev VI, Röckner M (2003)

On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds.

Sbornik: Mathematics 194(7-8): 969-978.","apa_indent":"Bogachev, V. I., & Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*, *194*(7-8), 969-978. doi:10.1070/SM2003v194n07ABEH000750

","chicago":"Bogachev, Vladimir I., and Röckner, Michael. 2003. “On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds”. *Sbornik: Mathematics* 194 (7-8): 969-978.

","apa":"Bogachev, V. I., & Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*, *194*(7-8), 969-978. doi:10.1070/SM2003v194n07ABEH000750","default":"Bogachev VI, Röckner M (2003)

*Sbornik: Mathematics* 194(7-8): 969-978.","mla":"Bogachev, Vladimir I., and Röckner, Michael. “On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds”. *Sbornik: Mathematics* 194.7-8 (2003): 969-978.","ieee":" V.I. Bogachev and M. Röckner, “On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds”, *Sbornik: Mathematics*, vol. 194, 2003, pp. 969-978.","ama":"Bogachev VI, Röckner M. On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*. 2003;194(7-8):969-978."},"publication_identifier":{"issn":["1064-5616"]},"issue":"7-8","isi":1}]