Skip to main content
Log in

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

Access this article

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

Instant access to the full article PDF.

References

  1. Cordes, H. O.,Self-Adjointnes of powers of powers of elliptic operators on non-compact manifolds. Math. Ann. 195, 257–272, (1972).

    Article  MATH  MathSciNet  Google Scholar 

  2. Devinatz, A.,Essential selfadjointnes of Schrödinger type operators. Preprint.

  3. Hellwig, G.,Differential operatoren der mathematischen Physik. Berlin, Gottingen, Heidelberg: Springer 1964.

    Google Scholar 

  4. Ikebe, T., Kato, T.,Uniqueness of self-adjoint extensions of singular elliptic differential operators. Arch. Rational Mech. Anal 9, 77–92, (1962).

    Article  MATH  MathSciNet  Google Scholar 

  5. Jörgens, K.,Wesentliche Selbstadjungiertheit singularer elliptischer Differentialoperatoren zweiter Ordnung in C o (G). Math. Scand. 15, 5–17, (1964).

    MATH  MathSciNet  Google Scholar 

  6. Kalf, H., Walter, J., Strongly singular potentials and essential self-adjointness of singular elliptic operators inC 0 (ℝn/{0}). J. Functional Analysis 10, 114–130, (1972).

    Article  MATH  MathSciNet  Google Scholar 

  7. Kato, T.,Schrodinger operators with singular potentials. Israel J. Math. 13, 135–148, (1972).

    MathSciNet  Google Scholar 

  8. Ladyz'enskaya, O. A., Ural'tseva, N. M.,Linear and quasilinear elliptic equations. New York: Academic Press (1968).

    Google Scholar 

  9. Laptev, S. A.,Closure in the metric of a generalized Dirichlet integral, J. Differential Equations 7, 557–564, (1971).

    Google Scholar 

  10. Maz'ya, W. G.,On the closure in the metric of a generalized Dirichlet integral (Russian), Zap. naucnikh sem. LOMI 5, 192, (1967).

    Google Scholar 

  11. Moser, J.,A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13, 457–468, (1960).

    MATH  MathSciNet  Google Scholar 

  12. Pucci, C.,Limitazioni per soluzioni di equazioni ellitiche. Ann. Mat. Pura Appl. 74, 15–30, (1966).

    Article  MATH  MathSciNet  Google Scholar 

  13. Protter, M. H., Weinberger, H. F.,Maximum principles in differential equations. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, (1967).

    Google Scholar 

  14. Simader, C. G.,Bemerkungen über Schrodinger Operatoren mit stark singularen Potentialen. Math. Z. 138, 53–70, (1974).

    Article  MATH  MathSciNet  Google Scholar 

  15. Simon, B.,Essential selfadjointness of Schrodinger operators with positive potentials. Math. Ann. 201, 211–220, (1973).

    Article  MATH  MathSciNet  Google Scholar 

  16. Stetkaer-Hansen, H.,A generalization of a theorem of Wienholtz concerning essential selfadjointness of singular elliptic operators. Math. Scand. 19, 108–112, (1966).

    MATH  MathSciNet  Google Scholar 

  17. Stummel, F.,Singulare elliptische Differentialoperatoren in Hilbertschen Raumen. Math. Ann. 132, 150–176, (1956).

    Article  MATH  MathSciNet  Google Scholar 

  18. Triebel, H.,Erzeugung nuklearer lokalkonvexer Raune durch singulare Differentialoperatoren zweiter Ordnung. Math. Ann. 174, 163–176, (1967).

    Article  MATH  MathSciNet  Google Scholar 

  19. Ural tseva, N. N., The non-selfadjointness inL 2(ℝn) of an elliptic operator with rapidly increasing coefficients (Russian). Zap. Naucn. Sem. Leningrad, Otedl. Mat. Inst Steklov, (LOMI) 14, 288–294, (1969).

    Google Scholar 

  20. Walter, J.,Symmetrie elliptischer Differentialoperatoren I, II. Math. Zeitschr. 98, 401–406, (1967); Math. Zeitschr. 106, 149–152 (1968).

    Article  MATH  Google Scholar 

  21. Walter, J.,Note on a paper by Stetkaer-Hansen concerning essential selfadjointness of Schrodinger operators. Math. Scand. 25, 94–96, (1969).

    MATH  MathSciNet  Google Scholar 

  22. Weyl, H.,Uber gewohnliche Differentialgleichungen mit Singularitaten und die zugehorigen Entwicklungen willkürlicher Funktionen. Math. Ann. 68, 220–269, (1910).

    Article  MathSciNet  Google Scholar 

  23. Widman, K. O.,The singularity of the Green function for nonuniformly elliptic partial differential equations with discontinuous coefficients. Technical report. Uppsala University 1970.

  24. Wienholtz, E.,Halbbeschrankte partielle Differential operatoren vom elliptischen Typus. Math. Ann. 135, 50–80, (1958).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors

Additional information

Supported by the National Science Foundation USA

About this article

Cite this article

Frehse, J. Essential selfadjointness of singular elliptic operators. Bol. Soc. Bras. Mat 8, 87–107 (1977). https://doi.org/10.1007/BF02584723

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02584723

Keywords

Navigation