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Uspekhi Mat. Nauk, 1970, Volume 25, Issue 4(154), Pages 29–56 (Mi umn5376)  

This article is cited in 10 scientific papers (total in 10 papers)

Degenerating elliptic differential and psevdo-differential operators

M. I. Vishik, V. V. Grushin


Abstract: The present paper is a survey of some results concerning higher-order elliptic differential operators which degenerate on the boundary of a domain. The principal aspect in the study of such operators is that of investigating the corresponding ordinary equations with parameters which degenerate at a single point. The parametrix for such operators is a degenerating pseudo-differential operator. We investigate the properties of the kernels of these pseudo-differential operators.

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English version:
Russian Mathematical Surveys, 1970, 25:4, 21–50

Bibliographic databases:

UDC: 517.43
MSC: 35J70, 35S15, 35J40, 47B34
Received: 03.03.1970

Citation: M. I. Vishik, V. V. Grushin, “Degenerating elliptic differential and psevdo-differential operators”, Uspekhi Mat. Nauk, 25:4(154) (1970), 29–56; Russian Math. Surveys, 25:4 (1970), 21–50

Citation in format AMSBIB
\Bibitem{VisGru70}
\by M.~I.~Vishik, V.~V.~Grushin
\paper Degenerating elliptic differential and psevdo-differential operators
\jour Uspekhi Mat. Nauk
\yr 1970
\vol 25
\issue 4(154)
\pages 29--56
\mathnet{http://mi.mathnet.ru/umn5376}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513039}
\zmath{https://zbmath.org/?q=an:0209.40901|0222.35024}
\transl
\jour Russian Math. Surveys
\yr 1970
\vol 25
\issue 4
\pages 21--50
\crossref{https://doi.org/10.1070/RM1970v025n04ABEH001260}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Egorov, “On the solubility of differential equations with simple characteristics”, Russian Math. Surveys, 26:2 (1971), 113–130  mathnet  crossref  mathscinet  zmath
    2. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:3 (1975), 55–105  mathnet  crossref  mathscinet  zmath
    3. P. R. Popivanov, “Local solvability of pseudodifferential operators with characteristics of second multiplicity”, Math. USSR-Sb., 29:2 (1976), 193–216  mathnet  crossref  mathscinet  zmath  isi
    4. S. Z. Levendorskii, “On types of degenerate elliptic operators”, Math. USSR-Sb., 66:2 (1990), 523–540  mathnet  crossref  mathscinet  zmath  isi
    5. M. Giona, A. Adrover, “Nonuniform Stationary Measure of the Invariant Unstable Foliation in Hamiltonian and Fluid Mixing Systems”, Phys Rev Letters, 81:18 (1998), 3864  crossref  adsnasa  isi
    6. A. Adrover, M. Giona, “Measure-theoretical properties of the unstable foliation of two-dimensional differentiable area-preserving systems”, Phys Rev E, 60:1 (1999), 347  crossref  mathscinet  adsnasa  isi
    7. Baev A.D., Sadchikov P.V., “Ob apriornykh otsenkakh reshenii kraevykh zadach, modeliruyuschikh nekotorye statsionarnye protsessy s vyrozhdeniem”, Sistemy upravleniya i informatsionnye tekhnologii, 2009, no. 4(38), 69–73
    8. A. D. Baev, S. S. Buneev, “A priori estimates of solutions of boundary value problems in a band for a class of degenerate elliptic equation of higher order”, Russian Math. (Iz. VUZ), 56:7 (2012), 44–46  mathnet  crossref  mathscinet
    9. A. D. Baev, S. S. Buneev, “Teorema o suschestvovanii i edinstvennosti resheniya odnoi kraevoi zadachi v polose dlya vyrozhdayuschegosya ellipticheskogo uravneniya vysokogo poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:3 (2012), 8–17  mathnet
    10. V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459  mathnet  crossref  mathscinet
  • Успехи математических наук Russian Mathematical Surveys
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