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Mat. Sb. (N.S.), 1977, Volume 103(145), Number 4(8), Pages 490–504 (Mi msb2923)  

This article is cited in 52 scientific papers (total in 52 papers)

The angular potential and some of its applications

S. A. Gabov


Abstract: In this paper a theory of the angular potential in Hölder classes is constructed, and several of its applications to problems in the theory of harmonic functions are considered.
Bibliography: 9 titles.

Full text: PDF file (1408 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1977, 32:4, 423–436

Bibliographic databases:

UDC: 519.947.42
MSC: Primary 35J05; Secondary 45B05
Received: 04.01.1977

Citation: S. A. Gabov, “The angular potential and some of its applications”, Mat. Sb. (N.S.), 103(145):4(8) (1977), 490–504; Math. USSR-Sb., 32:4 (1977), 423–436

Citation in format AMSBIB
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\by S.~A.~Gabov
\paper The angular potential and some of its applications
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 103(145)
\issue 4(8)
\pages 490--504
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=463457}
\zmath{https://zbmath.org/?q=an:0372.31002}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 4
\pages 423--436
\crossref{https://doi.org/10.1070/SM1977v032n04ABEH002396}
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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. Gabov S., “Spectrum and Bases From Eigenfunctions of One Problem of Acoustic-Oscillations of Rotating Liquid”, 254, no. 4, 1980, 777–779  mathscinet  zmath  isi
    2. Gabov S., “On the Spectrum of Sobolev,S.l. Problem”, 253, no. 3, 1980, 521–524  mathscinet  zmath  isi
    3. Gabov S., “On the Completeness and Basicity of the Eigenfunction System of a Problem Occurring in the Theory of Tidal Oscillations”, 250, no. 4, 1980, 780–782  mathscinet  zmath  isi
    4. Gabov S., “On the Theory of Harmonic Angular Potential”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1980, no. 5, 13–17  mathscinet  isi
    5. S. A. Gabov, “On the spectrum and bases of eigenfunctions of a problem connected with oscillations of a rotating fluid”, Math. USSR-Sb., 44:2 (1983), 219–226  mathnet  crossref  mathscinet  zmath
    6. Gabov S., Shevtsov P., “A Problem with a Spectral Parameter in the Boundary-Condition”, Differ. Equ., 18:4 (1982), 456–460  mathscinet  zmath  isi
    7. Shidlovsky A., Reztsov V., “Isotropization and Equivalenting of Nonhomogeneous Media with Reciprocal and Nonreciprocal Conductivity”, no. 8, 1984, 81–85  isi
    8. Gabov S., “Angular Potential for the Sobolev,S.l. Solution and its Applications”, 278, no. 3, 1984, 527–530  mathscinet  zmath  isi
    9. Gabov S., Pletner I., “On the Dirichlet Problem for the Gravitational-Gyroscopic Wave-Equation”, 295, no. 2, 1987, 272–275  mathscinet  isi
    10. P. A. Krutitskii, “The flow of electric current from rectilinear electrodes in a magnetized semiconductor film”, U.S.S.R. Comput. Math. Math. Phys., 30:6 (1990), 64–73  mathnet  crossref  mathscinet
    11. Yu. D. Pletner, “Structural properties of the solutions of the gravitational-gyroscopic wave equation and the explicit solution of a problem in the dynamics of a stratified rotating fluid”, U.S.S.R. Comput. Math. Math. Phys., 30:5 (1990), 167–177  mathnet  crossref  mathscinet  zmath
    12. P. A. Krutitskii, “Application of S. A. Gabov's potentials in semiconductor physics”, U.S.S.R. Comput. Math. Math. Phys., 31:1 (1991), 75–84  mathnet  mathscinet  isi
    13. Krutitskii P., “Equivalence of the Problem of the Directional Derivative and the Riemann–Hilbert Problem”, Differ. Equ., 28:5 (1992), 698–707  mathnet  mathscinet  zmath  isi
    14. P. A. Krutitskiǐ, “Dirichlet's problem for the Helmholtz equation outside cuts in a plane”, Comput. Math. Math. Phys., 34:8-9 (1994), 1073–1090  mathnet  mathscinet  zmath
    15. P. A. Krutitskiǐ, “The limit amplitude of the initial and boundary-value problem for an equation of composite type in a multiply connected domain”, Comput. Math. Math. Phys., 34:7 (1994), 951–957  mathnet  mathscinet  zmath  isi
    16. P.A.. Krutitskii, “An explicit solution of the pseudo-hyperbolic initial boundary value problem in a multiply connected region”, Math. Meth. Appl. Sci, 18:11 (1995), 897  crossref
    17. P. A. Krutitskii, “The 2-D Neumann problem in an exterior domain bounded by closed and open curves”, Math Meth Appl Sci, 20:18 (1997), 1551  crossref  mathscinet  zmath  isi
    18. A. B. Al'shin, Yu. D. Pletner, A. G. Sveshnikov, “Solvability of the transient analogue of the Lavrent'ev–Sedov–Keldysh problem for the ion-acoustic wave equation”, Comput. Math. Math. Phys., 37:12 (1997), 1474–1479  mathnet  mathscinet  zmath
    19. M. O. Korpusov, Yu. D. Pletner, A. G. Sveshnikov, “Unsteady waves in a stratified fluid excited by the variation of the normal velocity component on a line segment”, Comput. Math. Math. Phys., 37:9 (1997), 1076–1085  mathnet  mathscinet  zmath
    20. M. O. Korpusov, Yu. D. Pletner, A. G. Sveshnikov, “Oscillation of a two-sided line segment in a stratified fluid”, Comput. Math. Math. Phys., 37:8 (1997), 936–942  mathnet  mathscinet  zmath
    21. Krutitskii P., “A Mixed Problem for the Laplace Equation Outside a System of Cuts on the Plane”, Differ. Equ., 33:9 (1997), 1184–1193  mathnet  mathscinet  zmath  isi
    22. M. O. Korpusov, Yu. D. Pletner, A. G. Sveshnikov, “Oscillation of a set of curvilinear segments in a stratified fluid”, Comput. Math. Math. Phys., 38:9 (1998), 1519–1526  mathnet  mathscinet  zmath
    23. Al'shin A., Pletner Y., Sveshnikov A., “Unique Solvability of Dirichlet Task for Equation of Ionic-Acoustical Waves in Plasma”, Dokl. Akad. Nauk, 361:6 (1998), 749–751  mathnet  mathscinet  isi
    24. P. A. Krutitskii, “Scattering of tidal waves by a spit of an arbitrary shape”, Geophysical & Astrophysical Fluid Dynamics, 91:1-2 (1999), 85  crossref  elib
    25. P. A. Krutitskii, “The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts”, Proc Edin Math Soc, 43:2 (2000), 325  crossref  mathscinet  zmath  isi
    26. P. A. Krutitskii, “The integral representation for a solution of the 2-d Dirichlet problem with boundary data on closed and open curves”, Mathematika, 47:1-2 (2000), 339  crossref  mathscinet  zmath  isi
    27. P.A. Krutitskii, “The jump problem for the Helmholtz equation and singularities at the edges”, Applied Mathematics Letters, 13:4 (2000), 71  crossref
    28. Krutitskii P., Chikilev A., “The Method of Integral Equations in the Oblique Derivative Problem Arising in Semiconductor Physics”, Differ. Equ., 36:9 (2000), 1323–1336  mathnet  crossref  mathscinet  zmath  isi
    29. P. A. Krutitskii, “Scattering of tidal waves by reefs and spits”, Mathematika, 47:1-2 (2000), 355  crossref
    30. P. A. Krutitskii, “The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary”, Math. Notes, 69:6 (2001), 799–813  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    31. P.A. Krutitskii, “The Neumann Problem in a 2-D Exterior Domain with Cuts and Singularities at the Tips”, Journal of Differential Equations, 176:1 (2001), 269  crossref
    32. P.A. Krutitskii, “The jump problem for the Laplace equation”, Applied Mathematics Letters, 14:3 (2001), 353  crossref
    33. Krutitskii P., Sgibnev A., “The Method of Integral Equations in the Mixed Dirichlet-Neumann Problem for the Laplace Equation in the Exterior of Cuts in the Plane”, Differ. Equ., 37:10 (2001), 1363–1375  mathnet  crossref  mathscinet  zmath  isi
    34. Krutitskii P., “Method of Boundary Integral Equations in the Mixed Problem for the Laplace Equation with an Arbitrary Partition of the Boundary”, Differ. Equ., 37:1 (2001), 78–89  mathnet  crossref  mathscinet  zmath  isi
    35. Tchikilev A., Krutitskii P., “The Boundary Value Problem of the Physics of Magnetized Semiconductors in an Exterior Domain with Cuts”, Dokl. Math., 66:3 (2002), 385–389  zmath  isi
    36. Krutitskii P., Sgibnev A., “The Method of Integral Equations in the Generalized Jump Problem for the Laplace Equation Outside Cuts on the Plane”, Differ. Equ., 38:9 (2002), 1277–1292  mathnet  crossref  mathscinet  zmath  isi
    37. Krutitskii P., Sgibnev A., “Singularities of the Solution Gradient in the Generalized Jump Problem for the Laplace Equation Outside a Cut on the Plane”, Differ. Equ., 39:9 (2003), 1225–1236  mathnet  crossref  mathscinet  zmath  isi
    38. Krutitskii P., Tchikilev A., “Boundary Value Problem in the Physics of Magnetized Semiconductors in an Interior Domain with Cuts”, Dokl. Math., 67:2 (2003), 158–162  isi
    39. Sgibnev A., Krutitskii P., “The Mixed Problem for Harmonic Functions Outside a Cut of an Arbitrary Shape”, Progress in Analysis, Vols I and II, eds. Begehr H., Gilbert R., Wong M., World Scientific Publ Co Pte Ltd, 2003, 1151–1160  mathscinet  isi
    40. P.A. Krutitskii, “The mixed harmonic problem in a bounded cracked domain with Dirichlet condition on cracks”, Journal of Differential Equations, 198:2 (2004), 422  crossref
    41. Medkova D., “The Oblique Derivative Problem for the Laplace Equation in a Plain Domain”, Integr. Equ. Oper. Theory, 48:2 (2004), 225–248  crossref  mathscinet  zmath  isi
    42. P. A. Krutitskii, A. O. Chikilev, N. Ch. Krutitskaya, V. V. Kolybasova, “On a generalization of the Neumann problem for the Laplace equation outside cuts in a plane”, Math Meth Appl Sci, 28:5 (2005), 593  crossref  mathscinet  zmath  isi  elib
    43. P. A. Krutitskii, A. I. Sgibnev, “On the singularities of the gradient of the solution to the Dirichlet–Neumann problem outside a plane cut”, Math. Notes, 77:3 (2005), 335–347  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    44. P.A. Krutitskii, “The modified jump problem for the Laplace equation and singularities at the tips”, Journal of Computational and Applied Mathematics, 183:1 (2005), 232  crossref
    45. P.A. Krutitskii, “The mixed harmonic problem in an exterior cracked domain with Dirichlet condition on cracks”, Computers & Mathematics with Applications, 50:5-6 (2005), 769  crossref
    46. P. A. Krutitskii, A. I. Sgibnev, “The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane”, J. Math. Sci., 151:1 (2008), 2710–2725  mathnet  crossref  mathscinet  zmath  elib
    47. P. A. Krutitskii, D. Y. Kwak, Y. K. Hyon, “Numerical treatment of a skew-derivative problem for the Laplace equation in the exterior of an open arc”, J Eng Math, 59:1 (2007), 25  crossref  mathscinet  zmath  isi  elib
    48. Krutitskii P.A., “The Harmonic Problem in the Plane with Cuts Under Boundary Conditions of the Third Kind”, Dokl. Math., 77:1 (2008), 90–93  crossref  mathscinet  zmath  isi  elib
    49. C B Compean, M Kirchbach, “Momentum space trigonometric Rosen–Morse potential”, J Phys A Math Theor, 42:36 (2009), 365301  crossref  mathscinet  zmath  isi
    50. Krutitskii P.A., “Boundary value problem for the Laplace equation outside cuts on the plane with different conditions of the third kind on opposite sides of the cuts”, Differ. Equ., 45:1 (2009), 86–101  crossref  mathscinet  zmath  isi  elib  elib
    51. C B Compean, M Kirchbach, “On the exact solubility in momentum space of the trigonometric Rosen–Morse potential”, J Phys A Math Theor, 44:1 (2011), 015304  crossref
    52. P. A. Krutitskii, “Generalization of the Neumann problem to harmonic functions outside cuts on the plane”, Diff Equat, 49:9 (2013), 1062  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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