| 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 |
| . |
