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Matematicheskie Zametki, 2008, Volume 83, Issue 2, Pages 181–198
DOI: https://doi.org/10.4213/mzm3939 (Mi mzm3939) 		 
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
Full-text PDF (661 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm3939
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.
Received: 26.04.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 2, Pages 162–179
DOI: https://doi.org/10.1134/S0001434608010197
Bibliographic databases:
UDC: 517.9+519.217.4
Language: Russian
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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  • https://www.mathnet.ru/eng/mzm3939
  • https://doi.org/10.4213/mzm3939
  • https://www.mathnet.ru/eng/mzm/v83/i2/p181
    • This publication is cited in the following 2 articles:
    1. Arendt W., Kunkel S., Kunze M., “Diffusion with nonlocal boundary conditions”, J. Funct. Anal., 270:7 (2016), 2483–2507  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. L. Gurevich, “Elliptic problems with nonlocal boundary conditions and Feller semigroups”, Journal of Mathematical Sciences, 182:3 (2012), 255–440  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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