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Mathematics of the USSR-Sbornik, 1986, Volume 55, Issue 2, Pages 309–333
DOI: https://doi.org/10.1070/SM1986v055n02ABEH003007 (Mi sm1999) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Smoothness of generalized solutions of the equation $\widehat Hu=f$ and essential selfadjointness of the operator $\widehat H=-\sum_{i,j}\nabla_i a_{ij}\nabla_j+V$ with measurable coefficients

Yu. A. Semenov
English version PDF (1252 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM1986v055n02ABEH003007
Abstract: Certain aspects of the theory of second order elliptic partial differential operators are considered: $(L^p,L^q)$-estimates for powers of the resolvents, and the integralness and smoothness of certain linear spaces generated by solutions of such equations. Applications are given to the first spectral question. One of the main results is global criteria for essential selfadjointness in the presence of simultaneous growth at infinity of the coefficients determining the equation.
Bibliography: 21 titles.
Received: 28.12.1983
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1985, Volume 127(169), Number 3(7), Pages 311–335
Bibliographic databases:
UDC: 517.95
MSC: Primary 35J15, 35D10, 47F05; Secondary 47A10
Language: English
Original paper language: Russian
Citation: Yu. A. Semenov, “Smoothness of generalized solutions of the equation $\widehat Hu=f$ and essential selfadjointness of the operator $\widehat H=-\sum_{i,j}\nabla_i a_{ij}\nabla_j+V$ with measurable coefficients”, Mat. Sb. (N.S.), 127(169):3(7) (1985), 311–335; Math. USSR-Sb., 55:2 (1986), 309–333
Citation in format AMSBIB
\Bibitem{Sem85}
\by Yu.~A.~Semenov
\paper Smoothness of generalized solutions of the equation $\widehat Hu=f$ and essential selfadjointness of the operator $\widehat H=-\sum_{i,j}\nabla_i a_{ij}\nabla_j+V$ with measurable coefficients
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 127(169)
\issue 3(7)
\pages 311--335
\mathnet{http://mi.mathnet.ru/sm1999}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=798380}
\zmath{https://zbmath.org/?q=an:0603.35022}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 2
\pages 309--333
\crossref{https://doi.org/10.1070/SM1986v055n02ABEH003007}
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  • https://doi.org/10.1070/SM1986v055n02ABEH003007
  • https://www.mathnet.ru/eng/sm/v169/i3/p311
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:386
    Russian version PDF:113
    English version PDF:21
    References:71
     
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