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

Bogachev VI, Röckner M (2003)
Sbornik: Mathematics 194(7-8): 969-978.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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.
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Zeitschriftentitel
Sbornik: Mathematics
Band
194
Ausgabe
7-8
Seite(n)
969-978
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Bogachev VI, Röckner M. On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. Sbornik: Mathematics. 2003;194(7-8):969-978.
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
Bogachev, V. I., and Röckner, M. (2003). On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. Sbornik: Mathematics 194, 969-978.
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.
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.
Bogachev, V.I., Röckner, M.: On L-P-uniqueness of symmetric diffusion operators on Riemannian manifolds. Sbornik: Mathematics. 194, 969-978 (2003).
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.