On Schwarz-type boundary-value problems of polyanalytic equation on a triangle
Abstract
We will consider the Schwarz-type boundary-value problems (BVPs) of the polyanalytic equation on an isosceles orthogonal triangle. In contrast to [20], the expression of its unique solution is explicitly obtained by the different decomposition of polyanalytic functions.
References
M.B. Balk, Polyanalytic Functions, Akademie Verlag, Berlin, 2001.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, Jinyuan Du, Yufeng Wang, A Dirichlet problem for polyharmonic function, Ann. Mat. Pura Appl. 187 (2008), 435–457.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, G.N. Hile, A hierarchy of integral operators, Rocky Mountain J. Math. 27 (1997), 669–706.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, A. Kumar, Boundary value problem for inhomogeneous polyanalytic equation I, Analysis 25 (2005), 55–71.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, Boundary value problems in complex analysis I, Bol. Asoc. Mat. Venezolana 12 (2005), 65–85; II, Bol. Asoc. Mat. Venezolana 12 (2005), 217–250.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, Complex Analytic Methods for Partial Differential Equations: An Introductory Text, World Scientific, Singapore, 1994.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, T. Vaitekhovich, Green functions, reflections, and plane parqueting, preprint, FU Berlin, 2009.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, T. Vaitekhovich, Harmonic boundary value problems in the half disc and half ring, Funct. Approx. Comment. Math. 40 (2009), 251–282.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, C.J. Vanegas, Iterated Neumann problem for higher order Poisson equation, Math. Nachr. 279 (2006), 38–57.
##plugins.generic.googleScholarLinks.settings.viewInGS##
H. Begehr, D. Schmersau, The Schwarz problem for polyanalytic functions, Z. Anal. Anwendungen 24 (2005), 341–351.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jinyuan Du, Yufeng Wang, Riemann boundary value problems of polyanalytic functions and metaanalytic functions on the closed curves, Complex Var. Theory Appl. 50 (2005), 521–533.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jinyuan Du, Yufeng Wang, On boundary value problems of polyanalytic function on the real axis, Complex Var. Theory Appl. 48 (2003), 527–542.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A.S. Fokas, A unified transform method for solving linear and certain nonlinear PDEs, Proc. Roy. Soc. London Ser. A 453 (1997), 1411–1443.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jianke Lu, Boundary Value Problems for Analytic Functions, World Scientific, Singapore, 1993.
##plugins.generic.googleScholarLinks.settings.viewInGS##
N.I. Muskhelishvili, Singular Integral Equations, 2nd ed., Noordhoff, Groningen, 1968.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, Jinyuan Du, Haseman boundary value problem of bianalytic functions with different shifts on the unit circumference, J. Appl. Funct. Anal. 2 (2007), 147–158.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, Jinyuan Du, Hilbert boundary value problems of polyanalytic functions on the unit circumference, Complex Var. Elliptic Equ. 51 (2006), 923–943.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, Jinyuan Du, On Riemann boundary value problem of polyanalytic function on the real axis, Acta Math. Sci. Ser. B Engl. Ed. 24 (2004), 663–671.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, On modified Hilbert boundary-value problems of polyanalytic functions, Math. Methods Appl. Sci. 32 (2009), 1415–1427.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, Schwarz-type boundary value problems of polyanalytic function on the half unit disc, to appear.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Yufeng Wang, Yanjin Wang, Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle, to appear.
##plugins.generic.googleScholarLinks.settings.viewInGS##