On a class of degenerate elliptic operators arising from Fleming-Viot processes |
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Authors: | Sandra Cerrai Philippe Clément |
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Institution: | (1) Dip. Matematica per le Decisioni, Universitá di Firenze, Via C. Lombroso 6/17, I-50134 Firenze, Italy, e-mail: cerrai@cibs.sns.it, IT;(2) Dept. of Applied Mathematical Analysis, Technische Universiteit Delft, Mekelweg 4, 2628 CD Delft, The Netherlands, e-mail: ph.p.j.e.clement@its.tudelft.nl, NL |
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Abstract: | We are dealing with the solvability of an elliptic problem related to a class of degenerate second order operators which
arise from the theory of Fleming-Viot processes in population genetics. In the one dimensional case the problem is solved
in the space of continuous functions. In higher dimension we study the problem in spaces with respect to an explicit measure which, under suitable assumptions, can be taken invariant and symmetrizing for
the operators. We prove the existence and uniqueness of weak solutions and we show that the closure of the operator in such
spaces generates an analytic -semigroup.
Received December 4, 2000; accepted December 9, 2000. |
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Keywords: | : Fleming-Viot process degenerate elliptic problems generation of $ C_0 $-semigroups |
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