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Mat. Sb. (N.S.), 1976, Volume 101(143), Number 2(10), Pages 163–188 (Mi msb3894)  

This article is cited in 43 scientific papers (total in 43 papers)

On the boundary values of solutions of elliptic equations in domains with a smooth boundary

V. P. Mikhailov


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English version:
Mathematics of the USSR-Sbornik, 1976, 30:2, 143–166

Bibliographic databases:

UDC: 517.9
MSC: 35J67
Received: 10.06.1976

Citation: V. P. Mikhailov, “On the boundary values of solutions of elliptic equations in domains with a smooth boundary”, Mat. Sb. (N.S.), 101(143):2(10) (1976), 163–188; Math. USSR-Sb., 30:2 (1976), 143–166

Citation in format AMSBIB
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\by V.~P.~Mikhailov
\paper On the boundary values of solutions of elliptic equations in domains with a~smooth boundary
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 101(143)
\issue 2(10)
\pages 163--188
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\zmath{https://zbmath.org/?q=an:0345.35033}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 2
\pages 143--166
\crossref{https://doi.org/10.1070/SM1976v030n02ABEH001902}
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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. I. M. Petrushko, “On the boundary values of solutions of parabolic equations”, Math. USSR-Sb., 32:3 (1977), 347–370  mathnet  crossref  mathscinet  zmath  isi
    2. I. M. Petrushko, “On the boundary and initial values of solutions of parabolic equations”, Math. USSR-Sb., 35:1 (1979), 85–114  mathnet  crossref  mathscinet  zmath  isi
    3. A. K. Gushchin, V. P. Mikhailov, “On boundary values in $L_p$, $p>1$, of solutions of elliptic equations”, Math. USSR-Sb., 36:1 (1980), 1–19  mathnet  crossref  mathscinet  zmath  isi
    4. S. V. Gaidenko, “On exceptional sets on the boundary and the uniqueness of solutions of the Dirichlet problem for a second order elliptic equation”, Math. USSR-Sb., 39:1 (1981), 107–123  mathnet  crossref  mathscinet  zmath  isi
    5. Mikhailov V., “On the Boundary-Values of the Solutions of Elliptic-Equations”, Appl. Math. Optim., 6:3 (1980), 193–199  crossref  mathscinet  zmath  isi
    6. Kaliabin G., “Dirichlet Problem for Some Degenerating Elliptic-Equations with the Boundary Function From l+P”, 251, no. 2, 1980, 274–276  mathscinet  isi
    7. I. M. Petrushko, “On boundary values of solutions of elliptic equations in domains with Lyapunov boundary”, Math. USSR-Sb., 47:1 (1984), 43–72  mathnet  crossref  mathscinet  zmath
    8. Mikhailov YA., “Boundary-Values in Lp, P-Greater-Than-1, of Solutions of 2nd-Order Linear Elliptic-Equations”, Differ. Equ., 19:2 (1983), 243–258  isi
    9. Fedorova L., “Boundary-Values of Solutions for Inhomogeneous Differentially-Operator Equations”, no. 7, 1983, 21–24  mathscinet  isi
    10. S. V. Gaidenko, “On exceptional sets on the boundary and uniqueness of a solution of the second and third boundary value problems for an elliptic equation”, Math. USSR-Sb., 53:2 (1986), 351–366  mathnet  crossref  mathscinet  zmath
    11. Chabrowski J., “On the Dirichlet Problem for Semi-Linear Elliptic Equation with l2-Boundary Data”, Math. Z., 187:2 (1984), 171–183  crossref  mathscinet  zmath  isi
    12. Petrushko I., “The Boundary-Values of Solutions Degenerating at the Boundary of Domain of 2nd-Order Elliptic-Equations”, 284, no. 5, 1985, 1069–1073  mathscinet  zmath  isi
    13. Shelepov V., “Luzin Integral and Nontangential Maximal-Function in Domains Whose Boundaries Are Representable by the Difference of Convex-Functions”, 283, no. 4, 1985, 822–825  mathscinet  zmath  isi
    14. Chabrowski J., “On Boundary-Values of Solutions of a Quasi-Linear Partial-Differential Equation of Elliptic Type”, Rocky Mt. J. Math., 16:2 (1986), 223–236  crossref  mathscinet  zmath  isi
    15. V. Yu. Shelepov, “On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions”, Math. USSR-Sb., 61:2 (1988), 437–460  mathnet  crossref  mathscinet  zmath  isi
    16. Chabrowski J., “On the Dirichlet Problem for Degenerate Elliptic-Equations”, Publ. Res. Inst. Math. Sci., 23:1 (1987), 1–16  crossref  mathscinet  zmath  isi
    17. Hoffmannwalbeck T., “On the Dirichlet Problem for Linear Elliptic-Equations and Lp-Boundary Data, P-Greater-Than-1”, Boll. Unione Mat. Italiana, 1B:1 (1987), 1–30  mathscinet  isi
    18. I. M. Petrushko, “On boundary values of solutions of elliptic equations degenerating on the boundary”, Math. USSR-Sb., 64:1 (1989), 243–262  mathnet  crossref  mathscinet  zmath
    19. Chabrowski J., “Quasilinear Ellipticity and the Dirichlet Problem”, Isr. J. Math., 63:3 (1988), 353–379  crossref  mathscinet  zmath  isi
    20. Chabrowski J., “On the Solvability of the Dirichlet Problem for Nonlinear Elliptic-Equations”, J. Anal. Math., 50 (1988), 65–78  crossref  mathscinet  zmath  isi
    21. V. I. Gorbachuk, A. V. Knyazyuk, “Boundary values of solutions of operator-differential equations”, Russian Math. Surveys, 44:3 (1989), 67–111  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. A. K. Gushchin, V. P. Mikhailov, “On the existence of boundary values of solutions of an elliptic equation”, Math. USSR-Sb., 73:1 (1992), 171–194  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. L. A. Muravei, A. V. Filinovskii, “On a problem with nonlocal boundary condition for a parabolic equation”, Math. USSR-Sb., 74:1 (1993), 219–249  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    24. Chabrowski J., “Some Existence Theorems for the Dirichlet Problem for Quasi-Linear Elliptic-Equations”, Ann. Mat. Pura Appl., 158 (1991), 391–398  crossref  mathscinet  zmath  isi
    25. Petrushko I., “On Boundary-Values of Solutions of Parabolic Equations Degenerating on Domains Boundary”, 316, no. 3, 1991, 550–552  mathscinet  isi
    26. I. M. Petrushko, “Existence of boundary values for solutions of degenerate elliptic equations”, Sb. Math., 190:7 (1999), 973–1004  mathnet  crossref  crossref  mathscinet  zmath  isi
    27. Dumanian V., “Near-Boundary Behavior of the Solution to the Dirichlet Problem for an Elliptic Second-Order Equation”, Dokl. Math., 66:2 (2002), 257–259  mathscinet  isi
    28. Kapanadze D., “On the Representation of a Harmonic Function by a Simple Layer Potential”, Differ. Equ., 38:2 (2002), 259–262  mathnet  crossref  mathscinet  zmath  isi
    29. V. P. Mikhailov, “Existence of boundary values for biharmonic functions”, Sb. Math., 195:12 (2004), 1781–1793  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. Mikhailov, VP, “On the existence of limit values of a biharmonic function on the boundary of a domain”, Doklady Mathematics, 69:2 (2004), 228  isi  elib
    31. V. P. Mikhailov, “Existence of the boundary value of a polyharmonic function”, Siberian Math. J., 46:5 (2005), 902–912  mathnet  crossref  mathscinet  zmath  isi
    32. Mikhailov, VP, “On the existence of boundary limit values for solutions to polyharmonic equations”, Doklady Mathematics, 73:2 (2006), 261  crossref  isi  elib
    33. V. P. Mikhailov, “A sufficient condition for the existence of limit values of solutions of an elliptic equation on the boundary”, Theoret. and Math. Phys., 157:3 (2008), 1733–1744  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    34. A. R. Gerfanov, F. Kh. Mukminov, “Shirokii klass edinstvennosti resheniya dlya neravnomerno ellipticheskogo uravneniya v neogranichennoi oblasti”, Ufimsk. matem. zhurn., 1:3 (2009), 11–27  mathnet  zmath  elib
    35. V. Zh. Dumanyan, “Dirichlet weight integral estimation to Dirichlet problem solution for the general second order elliptic equations”, Uch. zapiski EGU, ser. Fizika i Matematika, 2009, no. 3, 10–21  mathnet
    36. V. P. Mikhailov, “Existence of boundary values of polyharmonic functions”, Sb. Math., 201:5 (2010), 735–757  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    37. V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    38. V. P. Mikhailov, “On Existence of a boundary value of a biharmonic function in a ball”, P-Adic Num Ultrametr Anal Appl, 4:1 (2012), 34  crossref
    39. I. M. Petrushko, M. I. Petrushko, “O pervoi smeshannoi zadache dlya vyrozhdayuschikhsya parabolicheskikh uravnenii s menyayuschimsya napravleniem vremeni”, Matematicheskie zametki SVFU, 23:1 (2016), 67–78  mathnet  elib
    40. Petrushko I.M., “On Boundary and Initial Values of Solutions of a Second-Order Parabolic Equation That Degenerate on the Domain Boundary”, Dokl. Math., 96:3 (2017), 568–570  crossref  isi
    41. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64  mathnet  crossref  crossref  isi  elib  elib
    42. N. A. Gusev, “On the definitions of boundary values of generalized solutions to an elliptic-type equation”, Proc. Steklov Inst. Math., 301 (2018), 39–43  mathnet  crossref  crossref  isi  elib  elib
    43. Petrushko I.M. Petrushko M.I., “On the First Mixed Problem in l-P, P > 1, For the Degenerating on the Boundary Parabolic Equations of Second Order”, AIP Conference Proceedings, 2048, ed. Pasheva V. Popivanov N. Venkov G., Amer Inst Physics, 2018, 040006  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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