Skip to main content
SpringerLink
Log in

Discontinuous solutions in problems of optimization

  • Part I Plenary Lectures
  • Conference paper
  • First Online:
Control Problems for Systems Described by Partial Differential Equations and Applications

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 97))

  • 140 Accesses

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Anzellotti and M. Giaquinta, Funzioni BV e tracce, Rend. Sem. Mat. Padova, 60 (1978), 1–21.

    Google Scholar 

  2. F. Cafiero, Criteri di compattezza per le successioni di funzioni generalmente a variazione limitata, Atti Accad. Naz. Lincei 8 (1950), 305–310.

    Google Scholar 

  3. L. Cesari, Sulle funzioni a variazione limitata, Ann. Scuola Norm. Sup. Pisa, 5 (1936), 299–313.

    Google Scholar 

  4. L. Cesari, Sulle funzioni di due variabili a variazione limitata e sulla convergenza delle serie doppie di Fourier, Rend. Sem. Mat. Univ. Roma, 1 (1937), 277–294

    Google Scholar 

  5. , Sulle funzioni di più variabili a variazione limitata e sulla convergenza delle relative serie multiple di Fourier, Pont. Accad. Scienze, Commentationes, 3 (1939), 171–197.

    Google Scholar 

  6. L. Cesari, Optimization-Theory and Applications, Problems with Ordinary Differential Equations, Springer Verlag (1983).

    Google Scholar 

  7. L. Cesari, P. Brandi and A. Salvadori, Existence theorems concerning simple integrals of the calculus of variations for discontinuous solutions, Arch. Rat. Mech. Anal. to appear.

    Google Scholar 

  8. L. Cesari, P. Brandi and A. Salvadori, Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions, to appear.

    Google Scholar 

  9. E. Conway and J. Smoller, Global solutions of the Cauchy problem for quasi-linear first-order equations in several space variables, Comm. Pure App. Math., 19 (1966), 95–105.

    Google Scholar 

  10. C.M. Dafermos, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26 (1977), 1097–1119.

    Google Scholar 

  11. P.J. Di Perna, Singularities of solutions of nonlinear hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal., 60 (1974), 75–100.

    Google Scholar 

  12. W.H. Fleming, Functions with generalized gradient and generalized surfaces, Ann. Math. Pure Appl., 44 (1957), 93–103.

    Google Scholar 

  13. E. Gagliardo, Proprietà di alcune classi di funzioni di più variabili, Ricerche Mat., 7 (1959), 24–51.

    Google Scholar 

  14. K. Krickeberg, Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nichtparametrischer Flächen, Ann. Mat. Pura Appl., 44 (1957), 105–133.

    Google Scholar 

  15. A.L. Volpert, The spaces BV and quasilinear equations, Mat. Sb. 73 (1967), 225–267.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Michigan, Ann Arbor, Michigan, USA

    L. Cesari

  2. Università degli Studi, Perugia, Italy

    P. Brandi & A. Salvadori

Authors
  1. L. Cesari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Brandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Salvadori
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Irena Lasiecka Roberto Triggiani

Rights and permissions

Reprints and permissions

Copyright information

© 1987 International Federation for Information Processing

About this paper

Cite this paper

Cesari, L., Brandi, P., Salvadori, A. (1987). Discontinuous solutions in problems of optimization. In: Lasiecka, I., Triggiani, R. (eds) Control Problems for Systems Described by Partial Differential Equations and Applications. Lecture Notes in Control and Information Sciences, vol 97. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038741

Download citation

  • DOI: https://doi.org/10.1007/BFb0038741

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18054-8

  • Online ISBN: 978-3-540-47722-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation