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Uspekhi Mat. Nauk, 1941, Issue 8, Pages 171–231 (Mi umn8823)  

This article is cited in 39 scientific papers (total in 39 papers)

Surveys and Translations
Series of papers on partial differential equations of the elliptic type

On the solubility and the stability of Dirichlet's problem

M. V. Keldysh


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Citation: M. V. Keldysh, “On the solubility and the stability of Dirichlet's problem”, Uspekhi Mat. Nauk, 1941, no. 8, 171–231

Citation in format AMSBIB
\Bibitem{Kel41}
\by M.~V.~Keldysh
\paper On the solubility and the stability of Dirichlet's problem
\jour Uspekhi Mat. Nauk
\yr 1941
\issue 8
\pages 171--231
\mathnet{http://mi.mathnet.ru/umn8823}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=5249}
\zmath{https://zbmath.org/?q=an:0179.43901}


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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. E. P. Dolzhenko, “O predstavlenii nepreryvnykh garmonicheskikh funktsii v vide potentsialov”, Izv. AN SSSR. Ser. matem., 28:5 (1964), 1113–1130  mathnet  mathscinet  zmath
    2. A. G. Vitushkin, “The analytic capacity of sets in problems of approximation theory”, Russian Math. Surveys, 22:6 (1967), 139–200  mathnet  crossref  mathscinet  zmath
    3. V. R. Nosov, “On a mixed problem for a hyperbolic equation of the second order”, Math. USSR-Izv., 3:2 (1969), 357–374  mathnet  crossref  mathscinet  zmath
    4. G. N. Blokhina, “Theorems of Phragmén–Lindelöf type for linear elliptic equations of second order”, Math. USSR-Sb., 11:4 (1970), 467–490  mathnet  crossref  mathscinet  zmath
    5. È. M. Saak, “A capacity criterion for a domain with stable Dirichlet problem for higher order elliptic equations”, Math. USSR-Sb., 29:2 (1976), 177–185  mathnet  crossref  mathscinet  zmath  isi
    6. E. A. Volkov, “An exponentially convergent method for the solution of Laplace's equation on polygons”, Math. USSR-Sb., 37:3 (1980), 295–325  mathnet  crossref  mathscinet  zmath  isi
    7. V. A. Kondrat'ev, O. A. Oleinik, “Boundary-value problems for partial differential equations in non-smooth domains”, Russian Math. Surveys, 38:2 (1983), 1–66  mathnet  crossref  mathscinet  zmath  isi
    8. A. I. Ibragimov, “On some qualitative properties of solutions of elliptic equations with continuous coefficients”, Math. USSR-Sb., 49:2 (1984), 447–460  mathnet  crossref  mathscinet  zmath
    9. A. A. Novruzov, “On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order”, Math. USSR-Sb., 50:2 (1985), 343–367  mathnet  crossref  mathscinet  zmath
    10. V. G. Maz'ya, S. A. Nazarov, “Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains”, Math. USSR-Izv., 29:3 (1987), 511–533  mathnet  crossref  mathscinet  zmath
    11. V. A. Kondrat'ev, O. A. Oleinik, “Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities”, Russian Math. Surveys, 43:5 (1988), 65–119  mathnet  crossref  mathscinet  zmath  isi
    12. V. A. Kondrat'ev, J. Kopáček, O. A. Oleinik, “On the continuity type on the boundary of nonregular domain of the generalized solution of the Dirichlet problem for biharmonic equation”, Math. USSR-Sb., 69:2 (1991), 607–620  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. P. V. Paramonov, “On harmonic approximation in the $C^1$-norm”, Math. USSR-Sb., 71:1 (1992), 183–207  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. N. N. Tarkhanov, “Approximation on compact sets by solutions of systems with surjective symbol”, Russian Math. Surveys, 48:5 (1993), 103–145  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. P. V. Paramonov, “$C^m$-approximations by harmonic polynomials on compact sets in $\mathbb R^n$”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 231–251  mathnet  crossref  mathscinet  zmath  isi
    16. N. O. Belova, “Spectral synthesis in Sobolev weighted spaces”, Math. Notes, 56:2 (1994), 856–858  mathnet  crossref  mathscinet  zmath  isi
    17. B. Zh. Ishchanov, “Generalization of Fedorov's theorem to $M$-harmonic functions”, Math. Notes, 56:5 (1994), 1132–1136  mathnet  crossref  mathscinet  zmath  isi
    18. P. V. Paramonov, K. Yu. Fedorovskiy, “Uniform and $C^1$-approximability of functions on compact subsets of $\mathbb R^2$ by solutions of second-order elliptic equations”, Sb. Math., 190:2 (1999), 285–307  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. K. Yu. Fedorovskiy, “Approximation and Boundary Properties of Polyanalytic Functions”, Proc. Steklov Inst. Math., 235 (2001), 251–260  mathnet  mathscinet  zmath
    20. E. A. Volkov, “A Method of Composite Grids on a Prism with an Arbitrary Polygonal Base”, Proc. Steklov Inst. Math., 243 (2003), 131–153  mathnet  mathscinet  zmath
    21. M. Ya. Mazalov, “Uniform approximations by bianalytic functions on arbitrary compact subsets of $\mathbb C$”, Sb. Math., 195:5 (2004), 687–709  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. M. Ya. Mazalov, “A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations”, Sb. Math., 199:1 (2008), 13–44  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    23. Galaktionov, VA, “On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach”, Nodea-Nonlinear Differential Equations and Applications, 16:5 (2009), 597  crossref  isi
    24. E. A. Volkov, “A two-stage difference method for solving the Dirichlet problem for the Laplace equation on a rectangular parallelepiped”, Comput. Math. Math. Phys., 49:3 (2009), 496–501  mathnet  crossref  mathscinet  isi  elib  elib
    25. M. Ya. Mazalov, “Uniform approximation by harmonic functions on compact subsets of $\mathbb R^3$”, J. Math. Sci. (N. Y.), 182:5 (2012), 674–689  mathnet  crossref
    26. M. Ya. Mazalov, “Uniform approximation problem for harmonic functions”, St. Petersburg Math. J., 23:4 (2012), 731–759  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    27. M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Conditions for $C^m$-approximability of functions by solutions of elliptic equations”, Russian Math. Surveys, 67:6 (2012), 1023–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. M. Ya. Mazalov, “Criterion of uniform approximability by harmonic functions on compact sets in $\mathbb R^3$”, Proc. Steklov Inst. Math., 279 (2012), 110–154  mathnet  crossref  mathscinet  isi  elib
    29. M. Ya. Mazalov, “O ravnomernoi priblizhaemosti resheniyami ellipticheskikh uravnenii poryadka vyshe dvukh”, Ufimsk. matem. zhurn., 4:4 (2012), 108–118  mathnet
    30. Fedorovskii K.Yu., “O ravnomernoi approksimatsii funktsii na ploskikh kompaktakh resheniyami odnorodnykh ellipticheskikh uravnenii”, Vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. seriya: estestvennye nauki, 2012, no. 3, 3–15  elib
    31. A. I. Parfenov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377  mathnet
    32. A. K. Guschin, “O zadache Dirikhle dlya ellipticheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 19–43  mathnet  crossref  zmath  elib
    33. A. K. Gushchin, “V.A. Steklov's work on equations of mathematical physics and development of his results in this field”, Proc. Steklov Inst. Math., 289 (2015), 134–151  mathnet  crossref  crossref  isi  elib
    34. A. K. Gushchin, “Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation”, Sb. Math., 206:10 (2015), 1410–1439  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. P. V. Paramonov, “New Criteria for Uniform Approximability by Harmonic Functions on Compact Sets in $\mathbb R^2$”, Proc. Steklov Inst. Math., 298 (2017), 201–211  mathnet  crossref  crossref  isi  elib
    36. M. Ya. Mazalov, “On Bianalytic Capacities”, Math. Notes, 103:4 (2018), 672–677  mathnet  crossref  crossref  mathscinet  isi  elib
    37. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    38. M. Ya. Mazalov, “A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients”, Sb. Math., 211:9 (2020), 1267–1309  mathnet  crossref  crossref  mathscinet  isi  elib
    39. P. V. Paramonov, “Ravnomernye approksimatsii funktsii resheniyami silno ellipticheskikh uravnenii vtorogo poryadka na kompaktakh v $\mathbb R^2$”, Matem. sb., 212:12 (2021), 77–94  mathnet  crossref
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