Skip to main content
SpringerLink
Log in

Nonlinear elliptic systems with dynamic boundary conditions

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Agmon, S., Douglis, A., Nierenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II. Commun. Pure Appl. Math.XVII, 35–92 (1964)

    Google Scholar 

  2. Amann, H.: Dual semigroup and second order linear elliptic boundary value problems. Isr. J. Math.45, 225–254 (1983)

    MATH  MathSciNet  Google Scholar 

  3. Amann, H.: Existence and regularity for semilinear parabolic evolution equations. Ann. Sc. Norm. Super. Pisa, IV. Ser.XI, 593–676 (1984)

    MathSciNet  Google Scholar 

  4. Amann, H.: Semigroups and nonlinear evolutions equations. Linear Algebra Appl.84, 3–32 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Amann, H.: Parabolic evolutions equations and nonlinear boundary conditions. J. Differ. Equations72, 201–269 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  6. Amann, H.: Parabolic evolution equation in interpolation and extrapolation spaces. J. Funct. Anal.78, 233–270 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  7. Amann, H.: Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems. Differ. Integral Equations3, 13–75 (1990)

    MATH  MathSciNet  Google Scholar 

  8. Bergh, J., Löfström, J.: Interpolation Spaces. An Introduction. Berlin Heidelberg New York: Springer 1976

    MATH  Google Scholar 

  9. Bony, J.-M.: Principle du maximum dans les espace de Sobolev. C.R. Acad. Sci., Paris, Sér. A265, 333–336 (1967)

    MATH  MathSciNet  Google Scholar 

  10. De Figueiredo, D.G.: The coercivness problem for forms over vector valued functions. Commun. Pure. Appl. Math.IVI, 63–94 (1963)

    Google Scholar 

  11. Diaz, J.I., Jimenez, R.F.: Application de la teoria no lineal de semigroup a un operator pseudodifferential. Actas VII C.E.D.Y.A., 137–142 (1984)

  12. Escher, J.: Global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions. Math. Ann.284, 285–305 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fattorini, H.O.: The Cauchy Problem. Reading, MA.: Addison-Wesley 1983

    Google Scholar 

  14. Friedmann, A., Shinbrot, M.: The initial value problem for the linearized equations of water waves. J. Math. Mech.17, 107–180 (1968)

    Google Scholar 

  15. Gajewski, H., Gröger, K., Zacharias, K.: Nichtlinear Operatorgleichungen und Operatordifferentialgleichungen. Berlin: Akademie-Verlag 1974

    Google Scholar 

  16. Geymonat, G., Grisvard, P.: Alcuni risultati di teoria spettrale per i problemi ai limiti lineari ellittici. Rend. Semin. Mat. Univ. Padova38, 121–173 (1967)

    MathSciNet  Google Scholar 

  17. Gröger, K.: Initial boundary value problems from semiconductor device theory. Z. Angew. Math. Mech.67, 345–355 (1987)

    MATH  MathSciNet  Google Scholar 

  18. Hintermann, T.: Evolution equation with dynamic boundary conditions. Proc. R. Soc. Edinb., Sect. A135, 43–60 (1989)

    MathSciNet  Google Scholar 

  19. Krein, S.G., Petunin, J.I., Semenov, E.M.: Interpolation of linear operators. (Transl. Math. Monogr., vol. 54) Providence, RI: Am. Math. Soc. 1982

    Google Scholar 

  20. Lions, J.-L.: Quelques Méthodes de Resolutions des Problémes aux Limites Non Lineaires. Paris: Dunod 1969

    Google Scholar 

  21. Lions, J.-L., Magenes, E.: Problemi ai limiti non omogenei V. Ann. Sc. Norm. Super, PisaXVI, 1–44 (1962)

    MathSciNet  Google Scholar 

  22. Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications I. Berlin Heidelberg New York: Springer 1972

    MATH  Google Scholar 

  23. Seeley, R.: Interpolation inL p with boundary conditions. Stud. Math.XLIV, 47–60 (1972)

    MathSciNet  Google Scholar 

  24. Showalter, R.: Degenerated evolution equations. Indiana Univ. Math. J.23, 655–677 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sobolevskii, P.E.: Equations of parabolic type in a Banach space. Tranl., II. Ser., Am. Math. Soc.49, 1–62 (1966)

    Google Scholar 

  26. Tanabe, H.: On the equation of evolution in a Banach space. Osaka Math. J.12, 363–376 (1960)

    MATH  MathSciNet  Google Scholar 

  27. Triebel, H.: Interpolation Theory, Function spaces, Differential Operators, Amsterdam: North Holland 1978

    Google Scholar 

  28. Wloka, J.: Partielle Differentialgleichungen. Stuttgart: Teubner 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    Joachim Escher

Authors
  1. Joachim Escher
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Escher, J. Nonlinear elliptic systems with dynamic boundary conditions. Math Z 210, 413–439 (1992). https://doi.org/10.1007/BF02571805

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571805

Keywords

Search

Navigation