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DOI :10.26650/ijmath.2025.00022   IUP :10.26650/ijmath.2025.00022    Tam Metin (PDF)

Dirihlet problem for the generalized Beltrami equation

Pelin Ayşe Gökgöz

In this article, we investigate the Dirichlet problem for the generalized Beltrami equation. Firstly, we introduce the solutions of the Dirichlet problem for the inhomogeneous Cauchy-Riemann equation in the unit disc. Secondly, we state the properties of the integral operators for regular domains. Then, by using Banach fixed point theorem, we obtain the existence of the unique solution of the Dirichlet problem for the generalized Beltrami equation in the unit disc.


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Referanslar

  • Aksoy, Ü., Çelebi, A.O., 2012, Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain, Complex Variables and Elliptic Equations, 57 2-4, 229-241. google scholar
  • Aksoy, Ü., Çelebi, A.O., 2010, Dirichlet problems for generalized /¡-Poisson equation, Oper. Theory Adv. Appl. 205, 129-142. google scholar
  • Begehr, H., 2005a, Boundary value problems in complex analysis I, Boletin de la Asociacion Matematica Venezolana, 12-1, 65-85. google scholar
  • Begehr, H., 2005b, Boundary value problems in complex analysis II. Boletin de la Asociacion Matematica Venezolana, 12-2, 217-250. google scholar
  • Begehr, H., Shupeyeva, B., 2021, Polyanalytic boundary value problems for planar domains with harmonic Green function, Analysis and Mathematical Physics, 11, 137. google scholar
  • Begehr, H.G.W., 1994, Complex Analytic Methods for Partial Differential Equations: An introductory text, World Scientific, Singapore. google scholar
  • Begehr, H., Vaitekhovich, T., 2012, Harmonic Dirichlet problem for some equilateral triangle, Complex Variables and Elliptic Equations, 57, 185-196. google scholar
  • Begehr, H., Gaertner, E., 2007, Dirichlet problem for the inhomogeneous polyharmonic equation in the upper half plane, Georgian Math J. 14, 33-52. google scholar
  • Begehr, H., Hile, G.N., 1997, A hierarchy of integral operators, Rocky Mountain J. Math. 27, 669-706. google scholar
  • Begehr, H., Harutyunyan, G., 2009, Neumann problem for the Beltrami operator and for second order operators with Poisson/Bitsadze operator as main part, Complex Variables and Elliptic Equations 54-12, 1129-1150. google scholar
  • Begehr, H., Obolashvili, E., 1994, Some boundary value problems for a Beltrami equation. Complex Variables and Elliptic Equations, 26, 1-2, 113-122. google scholar
  • Begehr, H., Vaitekhovich, T., 2007, Complex partial differential equations in a manner of I. N. Vekua. Lecture Notes of TICMI, 8, 15–26. google scholar
  • Gökgöz, P.A., 2024a, Dirichlet boundary value problem for linear polyanalytic equation in upper half plane, Complex Variables and Elliptic Equations, 70-4, 549–554. google scholar
  • Gökgöz, P.A., 2024b, Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane, Complex Analysis and Operator Theory 18, 121. google scholar
  • Harutyunyan, G., 2007, Boundary value problems for the Beltrami operator, Complex Variables and Elliptic Equations, 52-6, 475-484. google scholar
  • Tutschke, W., 1983, Partielle Differentialgleichungen - Klassiche, Funktionalanalytische und Komplexe Methoden, Teubner Texte zur Mathematics, Band 27, B.G. Teubner, Leipzig. google scholar
  • Vaitsiakhovich, T., 2008a, Boundary Value Problems for Complex Partial Differential Equations in a Ring Domain [Ph.D. thesis], Freie Universitat Berlin. google scholar
  • Vaitekhovich, T.S., 2008b, Boundary value problems to first-order complex partial differential equations, Integral Transforms and Special Functions, 19, 211-233. google scholar
  • Vaitekhovich, T., 2007, Boundary value problems to second order complex partial differential equations in a ring domain, Siauliai Mathematical Seminar, 2-10, 117-146. google scholar
  • Vekua, I.N., 1962, Generalized Analytic Functions. Pergamon Press, Oxford. google scholar
  • Yüksel, U., 2010, A Schwarz problem for the generalized Beltrami equation, Complex Variables and Elliptic Equations, 56-6, 503–511. google scholar
  • Wang, Y., Du, J., 2015, Harmonic Dirichlet problem in a ring sector. In: Current trends in analysis and its applications: Trends Math. Cham, Switzerland 67-75. google scholar

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APA

Gökgöz, P.A. (2025). Dirihlet problem for the generalized Beltrami equation. Istanbul Journal of Mathematics, 3(1), 12-19. https://doi.org/10.26650/ijmath.2025.00022


AMA

Gökgöz P A. Dirihlet problem for the generalized Beltrami equation. Istanbul Journal of Mathematics. 2025;3(1):12-19. https://doi.org/10.26650/ijmath.2025.00022


ABNT

Gökgöz, P.A. Dirihlet problem for the generalized Beltrami equation. Istanbul Journal of Mathematics, [Publisher Location], v. 3, n. 1, p. 12-19, 2025.


Chicago: Author-Date Style

Gökgöz, Pelin Ayşe,. 2025. “Dirihlet problem for the generalized Beltrami equation.” Istanbul Journal of Mathematics 3, no. 1: 12-19. https://doi.org/10.26650/ijmath.2025.00022


Chicago: Humanities Style

Gökgöz, Pelin Ayşe,. Dirihlet problem for the generalized Beltrami equation.” Istanbul Journal of Mathematics 3, no. 1 (Jul. 2025): 12-19. https://doi.org/10.26650/ijmath.2025.00022


Harvard: Australian Style

Gökgöz, PA 2025, 'Dirihlet problem for the generalized Beltrami equation', Istanbul Journal of Mathematics, vol. 3, no. 1, pp. 12-19, viewed 20 Jul. 2025, https://doi.org/10.26650/ijmath.2025.00022


Harvard: Author-Date Style

Gökgöz, P.A. (2025) ‘Dirihlet problem for the generalized Beltrami equation’, Istanbul Journal of Mathematics, 3(1), pp. 12-19. https://doi.org/10.26650/ijmath.2025.00022 (20 Jul. 2025).


MLA

Gökgöz, Pelin Ayşe,. Dirihlet problem for the generalized Beltrami equation.” Istanbul Journal of Mathematics, vol. 3, no. 1, 2025, pp. 12-19. [Database Container], https://doi.org/10.26650/ijmath.2025.00022


Vancouver

Gökgöz PA. Dirihlet problem for the generalized Beltrami equation. Istanbul Journal of Mathematics [Internet]. 20 Jul. 2025 [cited 20 Jul. 2025];3(1):12-19. Available from: https://doi.org/10.26650/ijmath.2025.00022 doi: 10.26650/ijmath.2025.00022


ISNAD

Gökgöz, PelinAyşe. Dirihlet problem for the generalized Beltrami equation”. Istanbul Journal of Mathematics 3/1 (Jul. 2025): 12-19. https://doi.org/10.26650/ijmath.2025.00022



ZAMAN ÇİZELGESİ


Gönderim18.02.2025
Kabul12.06.2025
Çevrimiçi Yayınlanma24.06.2025

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