On Green’s function of the Robin problem for the Poisson equation

References

[1] H. Begehr and T. Vaitekhovich, Modified harmonic Robin function, Complex Var. Elliptic Equ. 58 (2013), no. 4, 483–496. 10.1080/17476933.2011.625092Suche in Google Scholar

[2] A. V. Bitsadze, Equations of Mathematical Physics (in Russian), 2nd ed., “Nauka”, Moscow, 1982. Suche in Google Scholar

[3] E. Constantin and N. H. Pavel, Green function of the Laplacian for the Neumann problem in ℝ+n, Lib. Math. 30 (2010), 57–69. Suche in Google Scholar

[4] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Higher, Tricomi Transcendental Functions (Bateman Manuscript Project), McGraw-Hill, New York, 1953. Suche in Google Scholar

[5] T. S. Kal’menov, B. D. Koshanov and M. Y. Nemchenko, The Green function representation in the Dirichlet problem for polyharmonic equations in a ball, Dokl. Akad. Nauk 421 (2008), no. 3, 305–307. 10.1134/S1064562408040169Suche in Google Scholar

[6] T. S. Kal’menov and D. Suragan, On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation, Differ. Equ. 48 (2012), no. 3, 441–445. 10.1134/S0012266112030160Suche in Google Scholar

[7] V. V. Karachik, On one set of orthogonal harmonic polynomials, Proc. Amer. Math. Soc. 126 (1998), no. 12, 3513–3519. 10.1090/S0002-9939-98-05019-9Suche in Google Scholar

[8] V. V. Karachik, On an expansion of Almansi type, Math. Notes 83 (2008), no. 3–no. 4, 335–344. 10.1134/S000143460803005XSuche in Google Scholar

[9] V. V. Karachik, Construction of polynomial solutions of some boundary value problems for the Poisson’s equation, Comput. Math. Math. Phys. 51 (2011), no. 9, 1567–1587. 10.1134/S0965542511090120Suche in Google Scholar

[10] V. V. Karachik, On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball, J. Appl. Ind. Math. 8 (2014), no. 1, 63–75. 10.1134/S1990478914010074Suche in Google Scholar

[11] V. V. Karachik, Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball, Comput. Math. Math. Phys. 54 (2014), no. 7, 1122–1143. 10.1134/S0965542514070070Suche in Google Scholar

[12] V. V. Karachik, Green function of the Dirichlet boundary value problem for polyharmonic equation in a ball under polynomial data, Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 14 (2014), no. 4, 550–558. 10.18500/1816-9791-2014-14-4-550-558Suche in Google Scholar

[13] V. V. Karachik, Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball, Differ. Equ. 51 (2015), no. 8, 1033–1042. 10.1134/S0012266115080078Suche in Google Scholar

[14] V. V. Karachik, A Neumann-type problem for the biharmonic equation, Siberian Adv. Math. 27 (2017), no. 2, 103–118. 10.3103/S105513441702002XSuche in Google Scholar

[15] V. V. Karachik and N. A. Antropova, Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball, Differ. Equ. 49 (2013), no. 2, 251–256. 10.1134/S0012266113020122Suche in Google Scholar

[16] V. V. Karachik and B. T. Torebek, On the Dirichlet–Riquier problem for biharmonic equations, Math. Notes 102 (2017), no. 1–no. 2, 31–42. 10.1134/S0001434617070045Suche in Google Scholar

[17] M. A. Sadybekov, B. T. Torebek and B. K. Turmetov, Representation of Green’s function of the Neumann problem for a multi-dimensional ball, Complex Var. Elliptic Equ. 61 (2016), no. 1, 104–123. 10.1080/17476933.2015.1064402Suche in Google Scholar

[18] M. A. Sadybekov, B. T. Torebek and B. K. Turmetov, Representation of the Green’s function of the exterior Neumann problem for the Laplace operator, Sibirsk. Mat. Zh. 58 (2017), no. 1, 199–205. 10.1134/S0037446617010190Suche in Google Scholar

[19] M. A. Sadybekov, B. K. Turmetov and B. T. Torebek, On an explicit form of the Green function of the third boundary value problem for the Poisson equation in a circle, AIP Conf. Proc. 1611 (2014), 255–260. 10.1063/1.4893843Suche in Google Scholar

[20] M. A. Sadybekov, B. K. Turmetov and B. T. Torebek, On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle, Adv. Pure Appl. Math. 6 (2015), no. 3, 163–172. 10.1515/apam-2015-0003Suche in Google Scholar

[21] V. S. Vladimirov, Equations of Mathematical Physics, “Mir”, Moscow, 1984. Suche in Google Scholar

[22] Y. Wang, Tri-harmonic boundary value problems in a sector, Complex Var. Elliptic Equ. 59 (2014), no. 5, 732–749. 10.1080/17476933.2012.759566Suche in Google Scholar

[23] Y. Wang and L. Ye, Biharmonic Green function and biharmonic Neumann function in a sector, Complex Var. Elliptic Equ. 58 (2013), no. 1, 7–22. 10.1080/17476933.2010.551199Suche in Google Scholar