Skip to main content
Log in

Conditions under which the Cauchy problem is well posed for a given equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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.

Literature Cited

  1. A. M. Molchanov, “On conditions under which the spectrum of a self-adjoint differential equation of second order is discrete,” Tr. Mosk. Mat. Ob-va,2, 169–200 (1953).

    Google Scholar 

  2. M. Sh. Birman and B. S. Pavlov, “On the complete continuity of some imbedding operators,” Vestn. Leningr. Univ., Ser. Mat., Mekh., Astron., No. 1, 61–74 (1961).

    Google Scholar 

  3. V. G. Maz'ya, “On (p,l)-capacity, imbedding theorems, and the spectrum of a self-adjoint elliptic operator,” Izv. Akad. Nauk SSSR, Ser. Mat.,37, No. 2, 356–385 (1973).

    Google Scholar 

  4. V. G. Maz'ya, “The connection between two types of capacity,” Vestn. Leningr. Inst., Ser. Mat., Mekh., Astron., No. 7, 33–40 (1974).

    Google Scholar 

  5. M. Otelbaev, “The spectrum of a one-dimensional differential operator,” Vestn. Mosk. Univ., Ser. Mat., Mekh., No. 5, 59–66 (1972).

    Google Scholar 

  6. R. S. Strichartz, “Multipliers of fractional Sobolev spaces. I,” Math. Mech.,16, No. 9, 1031–1060 (1967).

    Google Scholar 

  7. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  8. V. G. Maz'ya, “Classes of sets and measures, connected with imbedding theorems,” in: Imbedding Theorems and Their Applications [in Russian], Nauka, Moscow (1970), pp. 142–159. (Proceedings of Symposium on Imbedding Theorems, Baku, 1966).

    Google Scholar 

  9. V. G. Maz'ya, “On removable singularities of bounded solutions of quasilinear elliptic equations of arbitrary order,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,26, 116–130 (1972).

    Google Scholar 

  10. D. R. Adams and J. C. Polking “The equivalence of two definitions of capacity,” Proc. Am. Math. Soc.,37, No. 2, 529–534 (1973).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 18, No. 5, pp. 1065–1072, September–October, 1977.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lavrent'ev, M.M., Amirov, A.K. Conditions under which the Cauchy problem is well posed for a given equation. Sib Math J 18, 753–770 (1977). https://doi.org/10.1007/BF00967013

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00967013

Keywords

Navigation