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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 181–198 (Mi mz3939)  

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

Full text: PDF file (661 kB)
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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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  • https://doi.org/10.4213/mzm3939
  • http://mi.mathnet.ru/eng/mz/v83/i2/p181

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
  • Математические заметки Mathematical Notes
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