Academic Journal of Engineering and Technology Science, 2019, 2(1); doi: 10.25236/AJETS.020018.
Yumei Li
Department of Mathematics, Jinan University, Guangzhou, China
*Corresponding author e-mail: [email protected]
In this article, we study polyharmonic fundamental solutions in Lipschitz graph domain in R2. By the ultraspherical polynomials and the definition of the polyharmonic fundamental solutions, we give a harmonic recursion formulate of the polyharmonic fundamental solutions.
Polyharmonic fundamental solutions, ultraspherical polynomials, Lipschitz graph domain
Yumei Li, Polyharmonic Fundamental Solutions in Lipschitz Graph Domain in R2. Academic Journal of Engineering and Technology Science (2019) Vol. 2: 85-91. https://doi.org/10.25236/AJETS.020018.
[1] Andrew G E, Askey R, Roy R. Special Function. Cambridge: Cambridge University Press, 1999.
[2] Du Z. Higher order Poisson Kernels and polyharmonic boudary value problems in Lipschitz domains. Sci China Math, to appear (arXiv: 1503. 01208).
[3] Du Z, Kou K, Wang J. polyharmonic Dirichlet problems in regular domains I: the unit disc. Complex Var Elliptic Equ, 2013, 58: 1387-1405.
[4] Du Z, Qian T, Wang J. polyharmonic Dirichlet problems in regular domains II: the upper-half plane. J Diffferential Equation, 2012, 252: 1789-1812.
[5] Du Z, Qian T, Wang J. polyharmonic Dirichlet problems in regular domains III: the unit ball. Complex Var Elliptic Equ, 2014, 59: 947-965.
[6] Du Z, Qian T, Wang J. polyharmonic Dirichlet problems in regular domains IV: the upper-half space. J Diffferential Equation, 2013, 255: 779-795.
[7] Du Z, Guo G, Pan K. An inhomogeneous polyharmonic Dirichlet problem with boundary data in the upper half-plane. Complex Var Elliptic Equ, 2017, 62: 1519-1540.
[8] G. Orthogonal Polynomials. AMS Colloquium, vol. 23. Providence R I: Amer Math Soc, 1975.