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Mat. Sb. (N.S.), 1969, Volume 79(121), Number 1(5), Pages 3–36 (Mi msb3576)  

This article is cited in 28 scientific papers (total in 28 papers)

On a class of higher order degenerate elliptic equations

M. I. Vishik, V. V. Grushin


Full text: PDF file (3355 kB)
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English version:
Mathematics of the USSR-Sbornik, 1969, 8:1, 1–32

Bibliographic databases:

UDC: 517.946.9
MSC: 35J70, 35J40, 35Sxx, 47E05, 35H30
Received: 24.12.1968

Citation: M. I. Vishik, V. V. Grushin, “On a class of higher order degenerate elliptic equations”, Mat. Sb. (N.S.), 79(121):1(5) (1969), 3–36; Math. USSR-Sb., 8:1 (1969), 1–32

Citation in format AMSBIB
\Bibitem{VisGru69}
\by M.~I.~Vishik, V.~V.~Grushin
\paper On~a~class of higher order degenerate elliptic equations
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 79(121)
\issue 1(5)
\pages 3--36
\mathnet{http://mi.mathnet.ru/msb3576}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=248454}
\zmath{https://zbmath.org/?q=an:0177.14302|0191.11703}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 1
\pages 1--32
\crossref{https://doi.org/10.1070/SM1969v008n01ABEH001276}


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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. M. I. Vishik, V. V. Grushin, “Boundary value problems for elliptic equations degenerate on the boundary of a domain”, Math. USSR-Sb., 9:4 (1969), 423–454  mathnet  crossref  mathscinet  zmath
    2. G. I. Èskin, “Degenerate elliptic pseudodifferential equations of principal type”, Math. USSR-Sb., 11:4 (1970), 539–582  mathnet  crossref  mathscinet  zmath
    3. V. V. Grushin, “On a class of hypoelliptic operators”, Math. USSR-Sb., 12:3 (1970), 458–476  mathnet  crossref  mathscinet  zmath
    4. V. V. Grushin, “Pseudodifferential operators on $\mathbf R^n$ with bounded symbols”, Funct. Anal. Appl., 4:3 (1970), 202–212  mathnet  crossref  mathscinet  zmath
    5. M. I. Vishik, V. V. Grushin, “Degenerating elliptic differential and psevdo-differential operators”, Russian Math. Surveys, 25:4 (1970), 21–50  mathnet  crossref  mathscinet  zmath
    6. V. S. Fedii, “On a criterion for hypoellipticity”, Math. USSR-Sb., 14:1 (1971), 15–45  mathnet  crossref  mathscinet  zmath
    7. A. V. Marchenko, “Ob indekse kraevykh zadach dlya vyrozhdayuschikhsya ellipticheskikh operatorov”, UMN, 26:6(162) (1971), 247–248  mathnet  mathscinet  zmath
    8. V. V. Grushin, “On a class of elliptic pseudodifferential operators degenerate on a submanifold”, Math. USSR-Sb., 13:2 (1971), 155–185  mathnet  crossref  mathscinet  zmath
    9. A. V. Marchenko, “On the index of boundary value problems for degenerate elliptic operators”, Math. USSR-Sb., 16:4 (1972), 615–634  mathnet  crossref  mathscinet  zmath
    10. V. V. Grushin, “Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols”, Math. USSR-Sb., 17:4 (1972), 497–514  mathnet  crossref  mathscinet  zmath
    11. F. Trèves, “On the local solubility of linear partial differential equations”, Russian Math. Surveys, 29:2 (1974), 263–292  mathnet  crossref  mathscinet  zmath
    12. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:2 (1975), 59–118  mathnet  crossref  mathscinet  zmath
    13. Slutski A., “On the Asymptotics of Solutions of Degenerative Elliptic-Equations with a Small Parameter at Higher Derivatives”, no. 3, 1981, 59–64  isi
    14. Baev A., “High-Order Degenerating Elliptic-Equations and Pseudodifferential-Operators Associated with Them”, 265, no. 5, 1982, 1044–1046  isi
    15. Fausto Segala, “Parametrices for operators of tricomi type”, Annali di Matematica, 140:1 (1985), 285  crossref  mathscinet  zmath  isi
    16. Omar Debbaj, “Regularite holderienne maximale de certains problems aux limites elliptiques singuliers”, Communications in Partial Differential Equations, 11:8 (1986), 1  crossref
    17. S. Z. Levendorskii, “On types of degenerate elliptic operators”, Math. USSR-Sb., 66:2 (1990), 523–540  mathnet  crossref  mathscinet  zmath  isi
    18. Omar Debbaj, “Regularite LPDes Problemes Aux Limites De Type Hermite Et Tricomi”, Communications in Partial Differential Equations, 16:1 (1991), 1  crossref
    19. S. A. Nazarov, “Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (sloping shell)”, Sb. Math., 191:7 (2000), 1075–1106  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. Schulze B.W., “Operator algebras with symbol hierarchies on manifolds with singularities”, Approaches to Singular Analysis - a Volume of Advances in Partial Differential Equations, Operator Theory : Advances and Applications, 125, 2001, 167–207  isi
    21. Egorov Yu.V., Chuong Nguyen Minh, Tuan Dang Anh, “On a semilinear degenerate elliptic boundary value problem for pseudodifferential equations”, Dokl. Math., 80:1 (2009), 456–459  mathnet  crossref  mathscinet  zmath  isi  elib
    22. Louis Boutet de Monvel, “Hypoelliptic operators with double characteristics and related pseudo-differential operators”, Comm Pure Appl Math, 27:5 (2010), 585  crossref
    23. Yu. V. Egorov, Nguyen Minh Chuong, Dang Anh Tuan, “A nonlinear boundary-value problem for a degenerate parabolic pseudodifferential equation”, J. Math. Sci. (N. Y.), 179:3 (2011), 461–474  mathnet  crossref  zmath  elib
    24. Baev A.D., Buneev S.S., “Ob odnom klasse kraevykh zadach v polose dlya vyrozhdayuschikhsya ellipticheskikh uravnenii vysokogo poryadka”, Doklady akademii nauk, 448:1 (2013), 7–7  elib
    25. Baev A.D. Buneev S.S., “On a Class of Boundary Value Problems in a Strip for Degenerate Higher-Order Elliptic Equations”, Dokl. Math., 87:1 (2013), 1–2  crossref  isi
    26. A. D. Baev, P. A. Kobylinskii, “On some properties of a class of degenerate pseudodifferential operators”, Dokl. Math, 91:1 (2015), 23  crossref
    27. A. D. Baev, R. A. Kovalevskiy, “Boundary value problems for a class of degenerate pseudodifferential equations”, Dokl. Math, 91:2 (2015), 131  crossref
    28. Baev A.D. Kovalevskii R.A. Kobylinskii P.A., “On degenerate elliptic equations of high order and pseudodifferential operators with degeneration”, Dokl. Math., 94:3 (2016), 659–662  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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