manuscripta mathematica

, Volume 28, Issue 1–3, pp 219–233 | Cite as

Variational inequalities with one-sided irregular obstacles

  • Jens Frehse
  • Umberto Mosco


The authors show that the Hölder continuity of the solutionu∈K≔{v∈H o 1 (Ω) | v≤ψ in Ω} of the variational inequality
$$(\triangledown u,\triangledown u - \triangledown v) \leqslant (f,u - v),v\varepsilon \mathbb{K},$$
also holds under a one-sided Hölder condition on the obstacle ψ. This class of obstacles ψ contains the implicit obstacles of the quasivariational inequalities occuring in stochastic impulse control.


Variational Inequality Number Theory Algebraic Geometry Topological Group Impulse Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bensoussan, A., and Lions, J. L.: C. R. Acad. Sci. Paris, série A276, 1411–1415, 1189–1192, 1333–1338 (1973) and ibidem, Bensoussan, A., and Lions, J. L.: C. R. Acad. Sci. Paris, série A278, 675–679, 747–751 (1974)Google Scholar
  2. [2]
    Brézis, H., and Stampacchia, G.: Sur la régularité de la solution d'inéquations elliptiques. Bull.Soc.Math.France96, 153–180 (1968)Google Scholar
  3. [3]
    Frehse, J., and Mosco, U.: Sur la régularité des solutions faibles de certaines inéquations variationnelles et quasi-variationnelles non-linéaires du contrôle stochastique. C.R.Acad.Sci.ParisGoogle Scholar
  4. [4]
    Gernhardt, R., and Bernstein, F. W.: Besternte Ernte. Obertshausen: Zweitausendundeins 1976Google Scholar
  5. [5]
    Hildebrandt, S., and Widman, K.-O.: On the Hölder continuity of quasi-linear elliptic systems of second order. Ann.Sc. Norm.Sup.Pisa (Ser.IV),4, 145–178 (1977)Google Scholar
  6. [6]
    Lewy, H.: On a refinement of Evans'law in potential theory. Acc.Naz.Lin.,Ser.VIII, Vol.XLVIII, fasc.1, 1970Google Scholar
  7. [7]
    Lewy, H., and Stampacchia, G.: On the regularity of the solution of a variational inequality. Comm.Pure Appl.Math.22, 153–188 (1969)Google Scholar
  8. [8]
    Morrey C.B., jr.: Multiple integrals in the calculus of variations. Die Grundlehren der mathematischen Wissenschaften 130. Berlin-Heidelberg-New York: Springer (1966)Google Scholar
  9. [9]
    Widman, K.-O.: Hölder continuity of solutions of elliptic systems. Manuscripta Math.5, 299–308 (1971)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jens Frehse
    • 1
  • Umberto Mosco
    • 2
  1. 1.Institut für Angewandte Mathematik der UniversitätBonn
  2. 2.Istituto MatematicoUniversità di RomaRoma

Personalised recommendations