Lototsky-Schnabl operators associated with a strictly elliptic differential operator and their corresponding Feller semigroup |
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Authors: | Marco Romito |
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Affiliation: | (1) Departimento di Matematica, Universitá di Pisa, Via Buonarroti 2, 56127 Pisa, Italia |
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Abstract: | Given an open bounded convex subset of p, a strictly elliptic differential operatorL and a continuous function, and denoted withTL the Dirichlet operator associated withL, the Lototsky-Schnabl operators associated withTL and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.Work supported by a C.N.R. Research Grant (n. 201.19.1, November 30, 1994) |
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Keywords: | 47D06 35K65 41A40 |
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