[{"intvolume":" 194","publication_identifier":{"issn":["1064-5616"]},"language":[{"iso":"eng"}],"type":"journal_article","date_created":"2010-04-28T12:58:45Z","user_id":"89573","citation":{"lncs":" Bogachev, V.I., Röckner, M.: On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. Sbornik: Mathematics. 194, 969-978 (2003).","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.","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.","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.

","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","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.","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.","ama":"Bogachev VI, Röckner M. On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics*. 2003;194(7-8):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.","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.","frontiers":"Bogachev, V. I., and Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. *Sbornik: Mathematics* 194, 969-978.","default":"Bogachev VI, Röckner M (2003)

*Sbornik: Mathematics* 194(7-8): 969-978."},"volume":194,"department":[{"_id":"10020"}],"article_type":"original","page":"969-978","publisher":"LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES","publication":"Sbornik: Mathematics","title":"On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds","date_updated":"2019-07-16T13:14:46Z","isi":1,"external_id":{"isi":["000186261600002"]},"quality_controlled":"1","doi":"10.1070/SM2003v194n07ABEH000750","abstract":[{"text":"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.","lang":"eng"}],"issue":"7-8","_id":"1609835","status":"public","publication_status":"published","author":[{"last_name":"Bogachev","first_name":"Vladimir I.","full_name":"Bogachev, Vladimir I."},{"id":"10585","full_name":"Röckner, Michael","last_name":"Röckner","first_name":"Michael"}],"year":"2003"}]
**