On a transform method for the Laplace equation in a polygon

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 68, Issue 4, 2003, Pages 355-408

  Fokas, A S ^a   Kapaev, A A ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Boundary value problems; Laplace equation; Poincar boundary conditions; Riemann Hilbert; Wiener Hopf

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONFORMAL MAPPING; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

KORTEWEG-DE VRIES EQUATION; LAPLACE EQUATION; POINCARE BOUNDARY CONDITIONS; RIEMANN-HILBERT PROBLEM;

LAPLACE TRANSFORMS;

EID: 0038720296     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/68.4.355     Document Type: Article

References (20)

1. Ablowitz, M. J. & Fokas, A. S. (1997) Complex Variables and Applications. Cambridge: Cambridge University Press.
2. Abrahams, I. D. (1998) On the non-commutative factorization of Wiener-Hopf kernels of Khrapkov type. Proc. R. Soc. Lond. A, 454, 1719-1743.
3. Antipov, Y. A. (1999) An exact solution of the 3-D-problem on an interface semi-infinite plane crack. J. Mech. Phys. Solids, 47, 1051-1093.
4. Antipo, Y. A. & Fokas, A. S. (2003) The modified Helmholtz equation in a semi-strip. Preprint.
5. Ben-Avraham, D. & Fokas, A. S. (2001) The solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence. Phys. Rev. E, 64, 016114.
6. Crowdy, D. & Fokas, A. S. (2003) Explicit integral solutions for the plane elastostatic semi-strip. Preprint.
7. Daniele, V. G. (1984) On the solution of two coupled Wiener-Hopf equations. SIAM J. Appl. Math., 44, 667-680.
8. Fokas, A. S. (2001) Two dimensional linear PDEs in a convex polygon. Proc. R. Soc. Lond. A, 457, 371-397.
9. Fokas, A. S. (2002) Differential forms, spectral theory and boundary value problems. The Legacy of the Inverse Scattering Transform. Providence: American Mathematical Society.
10. Fokas, A. S. & Kapaev, A. A. (2000) A Riemann-Hilbert approach to the Laplace equation. J. Math. Anal. Appl., 251, 770-804.
11. Fokas, A. S. & Zyskin, M. (2002) The fundamental differential form and boundary value problem. Quart. J. Mech. Appl. Math., 55, 457-479.
12. Fulton, S., Fokas, A. S. & Xenophontos, C. (2003) An analytical method for linear/elliptic equations and its numerical implementation. Preprint.
13. Gakhov, F. D. (1963) Boundary Problems. Moscow: Phys. Math. Publ.
14. Grisvard, P. (1985) Elliptic Problems in Non Smooth Domains. Boston, MA: Pitman.
15. Henkin, G. (1987) Method of integral representations in complex analysis. Encyclopedia of Mathematical Sciences, vol. 7. Berlin: Springer.
16. Jones, D. S. (1984) Commutative Wiener-Hopf factorization of a matrix. Proc. R. Soc. Lond. A, 393, 185-192.
17. Jones, D. S. (1986) Acoustics and Electromagnetic Waves. New York: Oxford University Press.
18. Moiseyev, N. G. (1980) Factorization of a matrix function of special form. Dokl. AN SSSR, 305, 44-47.
19. Noble, B. (1958) Methods Based on the Wiener-Hopf Techniques. New York: Pergamon.
20. Rawling, A. D. (1993) The Wiener-Hopf technique. Bull. IMA, 29, 102-105.