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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 3, Pages 15–28
DOI: https://doi.org/10.4213/faa114 (Mi faa114) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms

V. V. Zhikov

Vladimir State Pedagogical University
Full-text PDF (210 kB) Citations (37)
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DOI: https://doi.org/10.4213/faa114
Abstract: We give an example of an incompressible diffusion equation whose solution is nonunique. It is shown that this equation has an approximation solution as well as another solution that cannot be obtained by approximation. We give sufficient conditions for the uniqueness of a solution as well as for the uniqueness of an approximation solution.
Keywords: approximation solution, nonuniqueness, energy identity, maximal function, higher integrability.
Received: 12.09.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 3, Pages 173–183
DOI: https://doi.org/10.1023/B:FAIA.0000042802.86050.5e
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: Russian
Citation: V. V. Zhikov, “Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms”, Funktsional. Anal. i Prilozhen., 38:3 (2004), 15–28; Funct. Anal. Appl., 38:3 (2004), 173–183
Citation in format AMSBIB
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    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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