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This article is cited in 2 scientific papers (total in 2 papers)
Bounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Conditions near the Boundary
P. L. Gurevich Peoples Friendship University of Russia
Abstract:
We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure
of the domain with respect to a nonnegative Borel measure without assuming that the measure is small. We state sufficient conditions on the measure guaranteeing that the corresponding nonlocal operator is the generator of a Feller semigroup.
Keywords:
diffusion process, Feller semigroup, elliptic operator, Borel measure, Hille–Yosida theorem, nonlocal condition
DOI:
https://doi.org/10.4213/mzm3939
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English version:
Mathematical Notes, 2008, 83:2, 162–179
Bibliographic databases:
UDC:
517.9+519.217.4 Received: 26.04.2007
Citation:
P. L. Gurevich, “Bounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Conditions near the Boundary”, Mat. Zametki, 83:2 (2008), 181–198; Math. Notes, 83:2 (2008), 162–179
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz3939https://doi.org/10.4213/mzm3939 http://mi.mathnet.ru/eng/mz/v83/i2/p181
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
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P. L. Gurevich, “Elliptic problems with nonlocal boundary conditions and Feller semigroups”, Journal of Mathematical Sciences, 182:3 (2012), 255–440
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Arendt W., Kunkel S., Kunze M., “Diffusion with nonlocal boundary conditions”, J. Funct. Anal., 270:7 (2016), 2483–2507
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