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Mat. Sb. (N.S.), 1985, Volume 127(169), Number 3(7), Pages 311–335 (Mi msb1999)  

This article is cited in 3 scientific papers (total in 3 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


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.

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English version:
Mathematics of the USSR-Sbornik, 1986, 55:2, 309–333

Bibliographic databases:

UDC: 517.95
MSC: Primary 35J15, 35D10, 47F05; Secondary 47A10
Received: 28.12.1983

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/msb1999}
\mathscinet{http://www.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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    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. Yu. A. Semenov, “On the spectral theory of second-order elliptic differential operators”, Math. USSR-Sb., 56:1 (1987), 221–247  mathnet  crossref  mathscinet  zmath
    2. M. A. Perel'muter, Yu. A. Semenov, “Elliptic Operators Preserving Probability”, Theor. Probability Appl., 32:4 (1987), 718–721  mathnet  crossref  mathscinet  zmath
    3. Yu. B. Orochko, “The hyperbolic equation method in the theory of operators of Schrödinger type with a locally integrable potential”, Russian Math. Surveys, 43:2 (1988), 51–102  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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