RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1240 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

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} 

• http://mi.mathnet.ru/eng/msb1999
• http://mi.mathnet.ru/eng/msb/v169/i3/p311

 SHARE:

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
2. M. A. Perel'muter, Yu. A. Semenov, “Elliptic Operators Preserving Probability”, Theor. Probability Appl., 32:4 (1987), 718–721
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
•  Number of views: This page: 167 Full text: 48 References: 30