RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 1, Pages 101–160 (Mi izv2774)  

This article is cited in 5 scientific papers (total in 5 papers)

On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data

A. A. Kovalevskya, Yu. S. Gorbanb

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Donetsk National University

Abstract: We introduce the notions of $T$-solutions and shift $T$-solutions of variational inequalities corresponding to a non-linear degenerate anisotropic elliptic operator, a constraint set in a sufficiently large class, and an $L^1$-right-hand side. We prove theorems on the existence and uniqueness of such solutions and describe their properties. While the notion of $T$-solution is defined only when the constraint set contains at least one bounded function, the notion of shift $T$-solution does not require this condition. We describe the relation between these notions and prove that these types of solutions of a variational inequality coincide with ordinary solutions whenever the right-hand side is sufficiently regular.

Keywords: degenerate anisotropic elliptic variational inequalities, $L^1$-data, $T$-solution, shift $T$-solution, existence and uniqueness of solutions.

DOI: https://doi.org/10.4213/im2774

Full text: PDF file (961 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2011, 75:1, 101–156

Bibliographic databases:

UDC: 517.9
MSC: 35J85, 35J70, 35B65, 49J40
Received: 03.03.2008

Citation: A. A. Kovalevsky, Yu. S. Gorban, “On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data”, Izv. RAN. Ser. Mat., 75:1 (2011), 101–160; Izv. Math., 75:1 (2011), 101–156

Citation in format AMSBIB
\Bibitem{KovGor11}
\by A.~A.~Kovalevsky, Yu.~S.~Gorban
\paper On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data
\jour Izv. RAN. Ser. Mat.
\yr 2011
\vol 75
\issue 1
\pages 101--160
\mathnet{http://mi.mathnet.ru/izv2774}
\crossref{https://doi.org/10.4213/im2774}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2815997}
\zmath{https://zbmath.org/?q=an:1223.35180}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011IzMat..75..101K}
\elib{http://elibrary.ru/item.asp?id=20358779}
\transl
\jour Izv. Math.
\yr 2011
\vol 75
\issue 1
\pages 101--156
\crossref{https://doi.org/10.1070/IM2011v075n01ABEH002529}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000287579900005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053543554}


Linking options:
  • http://mi.mathnet.ru/eng/izv2774
  • https://doi.org/10.4213/im2774
  • http://mi.mathnet.ru/eng/izv/v75/i1/p101

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Kovalevsky A.A., Gorban Yu.S., “Solvability of degenerate anisotropic elliptic second-order equations with $L_1$-data”, Electron. J. Differential Equations, 2013, 167, 17 pp.  mathscinet  zmath  isi
    2. Yu. S. Gorban, A. A. Kovalevsky, “On the boundedness of solutions of degenerate anisotropic elliptic variational inequalities”, Results Math., 65:1-2 (2014), 121–142  crossref  mathscinet  zmath  isi  scopus
    3. A. A. Kovalevsky, “Toward the $L^1$-theory of degenerate anisotropic elliptic variational inequalities”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 156–172  mathnet  crossref  mathscinet  isi  elib
    4. A. A. Kovalevsky, “Integrability and boundedness of solutions to some anisotropic problems”, J. Math. Anal. Appl., 432:2 (2015), 820–843  crossref  mathscinet  zmath  isi  scopus
    5. Gorban Yu., “Existence of Entropy Solutions For Nonlinear Elliptic Degenerate Anisotropic Equations”, Open Math., 15 (2017), 768–786  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:560
    Full text:103
    References:55
    First page:23

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020