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

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.

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

Bibliographic databases:

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

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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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
2. Gabov S., “On the Spectrum of Sobolev,S.l. Problem”, 253, no. 3, 1980, 521–524
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
4. Gabov S., “On the Theory of Harmonic Angular Potential”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1980, no. 5, 13–17
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
6. Gabov S., Shevtsov P., “A Problem with a Spectral Parameter in the Boundary-Condition”, Differ. Equ., 18:4 (1982), 456–460
7. Shidlovsky A., Reztsov V., “Isotropization and Equivalenting of Nonhomogeneous Media with Reciprocal and Nonreciprocal Conductivity”, no. 8, 1984, 81–85
8. Gabov S., “Angular Potential for the Sobolev,S.l. Solution and its Applications”, 278, no. 3, 1984, 527–530
9. Gabov S., Pletner I., “On the Dirichlet Problem for the Gravitational-Gyroscopic Wave-Equation”, 295, no. 2, 1987, 272–275
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
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
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
13. Krutitskii P., “Equivalence of the Problem of the Directional Derivative and the Riemann–Hilbert Problem”, Differ. Equ., 28:5 (1992), 698–707
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
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
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
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
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
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
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
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
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
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
24. P. A. Krutitskii, “Scattering of tidal waves by a spit of an arbitrary shape”, Geophysical & Astrophysical Fluid Dynamics, 91:1-2 (1999), 85
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
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
27. P.A. Krutitskii, “The jump problem for the Helmholtz equation and singularities at the edges”, Applied Mathematics Letters, 13:4 (2000), 71
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
29. P. A. Krutitskii, “Scattering of tidal waves by reefs and spits”, Mathematika, 47:1-2 (2000), 355
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
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
32. P.A. Krutitskii, “The jump problem for the Laplace equation”, Applied Mathematics Letters, 14:3 (2001), 353
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
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
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
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
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
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
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
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
41. Medkova D., “The Oblique Derivative Problem for the Laplace Equation in a Plain Domain”, Integr. Equ. Oper. Theory, 48:2 (2004), 225–248
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
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
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
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
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
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
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
49. C B Compean, M Kirchbach, “Momentum space trigonometric Rosen–Morse potential”, J Phys A Math Theor, 42:36 (2009), 365301
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
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
52. P. A. Krutitskii, “Generalization of the Neumann problem to harmonic functions outside cuts on the plane”, Diff Equat, 49:9 (2013), 1062
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