Skip to main content

Non Regular Data in Unilateral Variational Problems

  • Chapter
Equilibrium Problems and Variational Models

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 68))

  • 466 Accesses

Abstract

I will describe here some results about “renormalized” (or “entropic”) solutions for unilateral nonlinear problems with L 1 or measure data, within the recent literature concerning such variational problems.

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

Access this chapter

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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. P. Bènilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre, J.L. Vasquez, An L 1 -Theory of Existence and Uniqueness of Solutions of Nonlinear Elliptic Equations, Ann. Sc. Norm. Sup. Pisa (4) 22 (1995) nr. 2, 241–273.

    Google Scholar 

  2. L. Boccardo, F. Murat, J.P. Puel, Existence of Bounded Solutions for Non Linear Elliptic Unilateral Problems, Ann. Mat. Pura Appl. (4) 152 (1988), 183–196.

    Article  MathSciNet  Google Scholar 

  3. L. Boccardo, G.R. Cirmi, Existence and Uniqueness of Solution of Unilateral Problems with L 1 Data, J. Convex Anal. 6(1999), no. 1, 195–206.

    MathSciNet  Google Scholar 

  4. L. Boccardo, T. Gallouët, L. Orsina,Existence and Uniqueness of Entropy Solutions for Nonlinear Elliptic Equations with Measure Data- Ann. Inst. H. Poincaré Anal. Non Linéaire13(1996), no. 5, 539–551.

    Google Scholar 

  5. G. Dal Maso, F. Murat, L. Orsina, A. Prignet,Definition and Existence of Renormalized Solutions of Elliptic Equations with General Measure Data -C. R. Acad. Sci. Paris Sér.I Math.325(1997).

    Google Scholar 

  6. R.J. Di Perna, P.L. Lions, On the Cauchy problem for Boltzman equations: Global existence and weak stability, Ann. of Math. 130 (1989), 321–366.

    Article  MathSciNet  Google Scholar 

  7. M. Fukushima, K. Sato, S. Taniguchi, On the closable part of pre-Dirichlet forms and the fine support of the underlying measures, Osaka J. Math. 13 (1996), 539–551.

    Google Scholar 

  8. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.

    MATH  Google Scholar 

  9. F. Murat, Soluciones renormalizadas de EDP elipticas no lineales, Publications du Laboratoire d’Analyse Numerique n. 93023, Université Pierre et Marie Curie, Paris (1993).

    Google Scholar 

  10. P. Oppezzi, A.M. Rossi, Existence of Solutions for Unilateral Problems with Multivalued Operators, J. Convex Anal. 2 (1995), 241–261.

    MathSciNet  Google Scholar 

  11. P. Oppezzi, A.M. Rossi, Esistenza di soluzioni per problemi unilateri con dato misura o in L 1, Ricerche Mat., XLV, 2 (1996), 491–513.

    MathSciNet  Google Scholar 

  12. P. Oppezzi, A.M. Rossi,Renormalized Solutions for Divergence Problems with L 1 Data, Atti Sem. Mat. Fis. Univ. Modena, Suppl. Vol. 46 (1998), 889–914.

    MathSciNet  Google Scholar 

  13. P. Oppezzi, A.M. Rossi, Unilateral Problems with Measure Data, to appear on Nonlinear Anal.

    Google Scholar 

  14. P. Oppezzi, A.M. Rossi, Unilateral problems with measure data: links and convergence, to appear on Diff. Int. Equations.

    Google Scholar 

  15. R.T. Rockafellar,Convex functions, monotone operators and variational inequalities, Theory and Applications of Monotone Operators, proc. NATO Institute (Venice, 1968), Oderisi, Gubbio, 1970, 35–65.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Oppezzi, P. (2003). Non Regular Data in Unilateral Variational Problems. In: Daniele, P., Giannessi, F., Maugeri, A. (eds) Equilibrium Problems and Variational Models. Nonconvex Optimization and Its Applications, vol 68. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0239-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0239-1_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7955-3

  • Online ISBN: 978-1-4613-0239-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics