Previous |  Up |  Next

Article

Title: Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation (English)
Author: Yuan, Hongfen
Author: Karachik, Valery V.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 72
Issue: 2
Year: 2022
Pages: 523-539
Summary lang: English
.
Category: math
.
Summary: Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem. (English)
Keyword: slice Clifford analysis
Keyword: slice Dirac equation
Keyword: Dirichlet problem
MSC: 30G35
MSC: 35J40
idZBL: Zbl 07547218
idMR: MR4412773
DOI: 10.21136/CMJ.2022.0043-21
.
Date available: 2022-04-21T19:04:31Z
Last updated: 2024-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/150415
.
Reference: [1] Altavilla, A., Bie, H. De, Wutzig, M.: Implementing zonal harmonics with the Fueter principle.J. Math. Anal. Appl. 495 (2021), Article ID 124764, 26 pages. Zbl 1460.30016, MR 4182974, 10.1016/j.jmaa.2020.124764
Reference: [2] Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis.Research Notes in Mathematics 76. Pitman, Boston (1982). Zbl 0529.30001, MR 0697564
Reference: [3] Cnudde, L., Bie, H. De: Slice Fourier transform and convolutions.Ann. Mat. Pura Appl. (4) 196 (2017), 837-862. Zbl 1378.30021, MR 3654935, 10.1007/s10231-016-0598-z
Reference: [4] Cnudde, L., Bie, H. De: Slice Segal-Bargmann transform.J. Phys. A, Math. Theor. 50 (2017), Article ID 255207, 23 pages. Zbl 1370.81089, MR 3663111, 10.1088/1751-8121/aa70ba
Reference: [5] Cnudde, L., Bie, H. De, Ren, G.: Algebraic approach to slice monogenic functions.Complex Anal. Oper. Theory 9 (2015), 1065-1087. Zbl 1322.30017, MR 3346770, 10.1007/s11785-014-0393-z
Reference: [6] Colombo, F., Lávička, R., Sabadini, I., Souček, V.: The Radon transform between monogenic and generalized slice monogenic functions.Math. Ann. 363 (2015), 733-752. Zbl 1335.30017, MR 3412341, 10.1007/s00208-015-1182-3
Reference: [7] Colombo, F., Sabadini, I., Struppa, D. C.: Slice monogenic functions.Isr. J. Math. 171 (2009), 385-403. Zbl 1172.30024, MR 2520116, 10.1007/s11856-009-0055-4
Reference: [8] Colombo, F., Sabadini, I., Struppa, D. C.: Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions.Progress in Mathematics 289. Birkhäuser, Basel (2011). Zbl 1228.47001, MR 2752913, 10.1007/978-3-0348-0110-2
Reference: [9] Delanghe, R.: Clifford analysis: History and perspective.Comput. Methods Funct. Theory 1 (2001), 107-153. Zbl 1011.30045, MR 1931607, 10.1007/BF03320981
Reference: [10] Delanghe, R., Sommen, F., Souček, V.: Clifford Algebra and Spinor-Valued Functions: A Function Theory for the Dirac Operator.Mathematics and Its Applications 53. Kluwer Academic Publishers, Dordrecht (1992). Zbl 0747.53001, MR 1169463, 10.1007/978-94-011-2922-0
Reference: [11] Dirichlet, P. G. L.: Über einen neuen Ausdruck zur Bestimmung der Dichtigkeit einer unendlich dünnen Kugelschale, wenn der Werth des Potentials derselben in jedem Punkte ihrer Oberfläche gegeben ist.Abh. Königlich, Preuss. Akad. Wiss. (1850), 99-116 German.
Reference: [12] Fueter, R.: Die Funktionentheorie der Differentialgleichungen $\Delta u = 0$ und $\Delta\Delta u = 0$ mit vier reellen Variablen.Comment. Math. Helv. 7 (1934), 307-330 German. Zbl 0012.01704, MR 1509515, 10.1007/BF01292723
Reference: [13] Gentili, G., Struppa, D. C.: A new approach to Cullen-regular functions of a quaternionic variable.C. R., Math., Acad. Sci. Paris 342 (2006), 741-744. Zbl 1105.30037, MR 2227751, 10.1016/j.crma.2006.03.015
Reference: [14] Ghiloni, R., Perotti, A.: Volume Cauchy formulas for slice functions on real associative *-algebras.Complex Var. Elliptic Equ. 58 (2013), 1701-1714. Zbl 1277.30038, MR 3170730, 10.1080/17476933.2012.709851
Reference: [15] Huang, S., Qiao, Y. Y., Wen, G. C.: Real and Complex Clifford Analysis.Advances in Complex Analysis and its Applications 5. Springer, New York (2006). Zbl 1096.30042, MR 2180036, 10.1007/b105856
Reference: [16] Karachik, V. V.: Polynomial solutions to systems of partial differential equations with constant coefficients.Yokohama Math J. 47 (2000), 121-142. Zbl 0971.35014, MR 1763777
Reference: [17] Karachik, V. V.: Method of Normalized Systems of Functions.Publishing center of SUSU, Chelaybinsk (2014), Russian. Zbl 1297.35005
Reference: [18] Karachik, V. V.: Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball.Differ. Equ. 51 (2015), 1033-1042. Zbl 1331.35118, MR 3404090, 10.1134/S0012266115080078
Reference: [19] Karachik, V. V., Turmetov, B.: Solvability of some Neumann-type boundary value problems for biharmonic equations.Electron. J. Differ. Equ. 2017 (2017), Article ID 218, 17 pages. Zbl 1371.35074, MR 3711171
Reference: [20] Perotti, A.: Almansi theorem and mean value formula for quaternionic slice-regular functions.Adv. Appl. Clifford Algebr. 30 (2020), Article ID 61, 11 pages. Zbl 1461.30118, MR 4140056, 10.1007/s00006-020-01078-4
Reference: [21] Perotti, A.: Almansi-type theorems for slice-regular functions on Clifford algebras.Complex Var. Elliptic Equ. 66 (2021), 1287-1297. Zbl 07409850, MR 4296802, 10.1080/17476933.2020.1755967
Reference: [22] Yuan, H.: Riquier and Dirichlet boundary value problems for slice Dirac operators.Bull. Korean Math. Soc. 55 (2018), 149-163. Zbl 1394.30038, MR 3761589, 10.4134/BKMS.b160905
.

Files

Files Size Format View
CzechMathJ_72-2022-2_13.pdf 255.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo