Skip to main content
SpringerLink
Log in

On the Extremal Regularization of the Variational Inequalities with Multivalued Operators

  • Conference paper
Differential Operators and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 117))

  • 338 Accesses

Abstract

In this paper we propose the method of solving of the variational inequalities with multivalued operators by some extremal problems. These extremal problems consist the inclusion with para-meter and the penalty function. As examples we consider the free boundary problems on W 1p (Ω), p ≥ 3.

The present research work was partially supported by ISF Grant PSU061103.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhauser, 1990.

    MATH  Google Scholar 

  2. V. Barbu, Analysis and control of non-linear infinite dimensional systems. Acad. Press, Inc., 1995.

    Google Scholar 

  3. F.E. Browder and P. Hess, Nonlinear Mappings of Monotone Type in Banach Spaces. J. Func. Anal., vol. 11, N2 (1972), pp. 251–294.

    Article  MathSciNet  Google Scholar 

  4. F. Clarce, Optimization and Nonsmooth Analysis.,John Willey & Sons, Inc., 1983.

    Google Scholar 

  5. Yu.A. Dubinsky, Nonlinear elliptic and parabolic equations. Itogi nauki i techniki: VINITI. Sovremennye problemy matematiki, vol. 9 (1976), pp. 5–130. (in Russian).

    Google Scholar 

  6. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holand Publ. Company, 1976.

    MATH  Google Scholar 

  7. V.I. Ivanenko and V.S. Melnik, Variational Methode in Control Problems for Distributed Systems. Kiev: Naukova dumka (in Russian), 1988.

    Google Scholar 

  8. N.N. Ladyzhenskaya and O.A. Uraltseva, Linear and quasilinear elliptic type equations. Moskou: Nauka (in Russian), 1973.

    MATH  Google Scholar 

  9. G.I. Laptev, First boundary-value problem for quasilinear elliptic equation with double degeneration. Differential equation, vol. 30, no. 6 (1994), pp. 1057–1068. (in Russian).

    MathSciNet  Google Scholar 

  10. J.-L. Lions, Quelques Methodes de Resolution de Problemes aux Limities Non Lineaires. Paris: Dunod, 1969.

    Google Scholar 

  11. V.S. Mel’nik and O.V. Solonoukha, On statiomary variational inequality with multivalued operators. ibernetica i systemny analis, no. 3 (1997), pp. 74–89. (in Russian).

    Google Scholar 

  12. O.V. Solonoukha, On Extremal Problem of the Variational Inequalities Regularization. Applied Mathematics and Computer Science, vol. 6, no. 4 (1996). pp. 733–752.

    MathSciNet  MATH  Google Scholar 

  13. O.V. Solonoukha, On the Stationary Variational Inequalities with the Generalized Pseudomonotone Operators. Method of finctional analysis and Topology, vol. 3, no. 4 (1997), pp. 81–95.

    MathSciNet  MATH  Google Scholar 

  14. O.V. Solonoukha, On Extremal Regularization of Optimization Problems which are Described by Variational Inequalities with Multivalued Operators. Kibernetika i vychislitelnaya technika, vol. 118 (1998) (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Simulation of Economical Systems, National Technical University of Ukraine “KPI”, Pr. Pobedy, 37, Kiev, 252056, Ukraine

    O. V. Solonoukha

Authors
  1. O. V. Solonoukha
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    I. Gohberg

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    M. Gorbachuk  & V. Gorbachuk  & 

  4. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  5. Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/1411, 1040, Vienna, Austria

    H. Langer

  6. Institute of Mathematics, Economics and Mechanics, Odessa State University, 270057, Dvoryanskaya str. 2, Odessa, Ukraine

    G. Popov

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Basel AG

About this paper

Cite this paper

Solonoukha, O.V. (2000). On the Extremal Regularization of the Variational Inequalities with Multivalued Operators. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8403-7_27

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9552-1

  • Online ISBN: 978-3-0348-8403-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation