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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 164–179
(Mi tm592)
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This article is cited in 2 scientific papers (total in 2 papers)
On the Existence of a Feller Semigroup with Atomic Measure in a Nonlocal Boundary Condition
P. L. Gurevich Peoples Friendship University of Russia
Abstract:
The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. An elliptic operator of second order is considered on a plane bounded region $G$. Its domain of definition consists of continuous functions satisfying a nonlocal condition on the boundary of the region. In general, the nonlocal term is an integral of a function over the closure of the region $G$ with respect to a nonnegative Borel measure $\mu(y,d\eta)$, $y\in\partial G$. It is proved that the operator is a generator of a Feller semigroup in the case where the measure is atomic. The smallness of the measure is not assumed.
Received in July 2007
Citation:
P. L. Gurevich, “On the Existence of a Feller Semigroup with Atomic Measure in a Nonlocal Boundary Condition”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 164–179; Proc. Steklov Inst. Math., 260 (2008), 157–171
Linking options:
https://www.mathnet.ru/eng/tm592 https://www.mathnet.ru/eng/tm/v260/p164
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Abstract page: | 308 | Full-text PDF : | 90 | References: | 58 | First page: | 9 |
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