Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 523-539
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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.
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.
DOI : 10.21136/CMJ.2022.0043-21
Classification : 30G35, 35J40
Keywords: slice Clifford analysis; slice Dirac equation; Dirichlet problem
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Yuan, Hongfen; Karachik, Valery V. Solutions of the generalized Dirichlet problem  for the iterated slice Dirac equation. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 523-539. doi: 10.21136/CMJ.2022.0043-21

[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. | DOI | MR | JFM

[2] Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Research Notes in Mathematics 76. Pitman, Boston (1982). | MR | JFM

[3] Cnudde, L., Bie, H. De: Slice Fourier transform and convolutions. Ann. Mat. Pura Appl. (4) 196 (2017), 837-862. | DOI | MR | JFM

[4] Cnudde, L., Bie, H. De: Slice Segal-Bargmann transform. J. Phys. A, Math. Theor. 50 (2017), Article ID 255207, 23 pages. | DOI | MR | JFM

[5] Cnudde, L., Bie, H. De, Ren, G.: Algebraic approach to slice monogenic functions. Complex Anal. Oper. Theory 9 (2015), 1065-1087. | DOI | MR | JFM

[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. | DOI | MR | JFM

[7] Colombo, F., Sabadini, I., Struppa, D. C.: Slice monogenic functions. Isr. J. Math. 171 (2009), 385-403. | DOI | MR | JFM

[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). | DOI | MR | JFM

[9] Delanghe, R.: Clifford analysis: History and perspective. Comput. Methods Funct. Theory 1 (2001), 107-153. | DOI | MR | JFM

[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). | DOI | MR | JFM

[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.

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[14] Ghiloni, R., Perotti, A.: Volume Cauchy formulas for slice functions on real associative *-algebras. Complex Var. Elliptic Equ. 58 (2013), 1701-1714. | DOI | MR | JFM

[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). | DOI | MR | JFM

[16] Karachik, V. V.: Polynomial solutions to systems of partial differential equations with constant coefficients. Yokohama Math J. 47 (2000), 121-142. | MR | JFM

[17] Karachik, V. V.: Method of Normalized Systems of Functions. Publishing center of SUSU, Chelaybinsk (2014), Russian. | JFM

[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. | DOI | MR | JFM

[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. | MR | JFM

[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. | DOI | MR | JFM

[21] Perotti, A.: Almansi-type theorems for slice-regular functions on Clifford algebras. Complex Var. Elliptic Equ. 66 (2021), 1287-1297. | DOI | MR | JFM

[22] Yuan, H.: Riquier and Dirichlet boundary value problems for slice Dirac operators. Bull. Korean Math. Soc. 55 (2018), 149-163. | DOI | MR | JFM

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