The Dbar formalism for certain linear non-homogeneous elliptic PDEs in two dimensions

European Journal of Applied Mathematics

Volumn 17, Issue 3, 2006, Pages 323-346

  Fokas, A S ^a   Pinotsis, D A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750290227     PISSN: 09567925     EISSN: 14694425     Source Type: Journal    
DOI: 10.1017/S0956792506006607     Document Type: Article

References (18)

1. ABLOWITZ, M. J. & FOKAS, A. S. (2003) Introduction and Applications of Complex Variables, 2nd ed. Cambridge University Press.
2. BEALS, R. & COIFMAN, R. (1989) Linear spectral problems, nonlinear equations and the Dbar method. Inverse Problems, 5, 87-130.
3. CROWDY, D. & FOKAS, A. S. (2004) Explicit integral solutions for the plane elastostatic semi-strip. Proc. R. Soc. Lond. A, 460, 1285-1309.
4. FOKAS, A. S. (1997) A unified transform method for solving linear and certain nonlinear PDEs. Proc. R. Soc. Lond. A, 453, 1411-1443.
5. FOKAS, A. S. (2000) On the integrability of linear and nonlinear partial differential equations. JMP, 41(6), 4188.
6. FOKAS, A. S. & KAPAEV, A. A. (2003) On a transform method for the Laplace equation in a polygon. IMA J. Appl. Math. 68, 355.
7. FOKAS, A. S. & PELLONI, B. (2000) A method of solving moving boundary value problems for linear evolution equations. Phys. Rev. Lett. 84, 4785.
8. FOKAS, A. S. & PELLONI, B. (2000) Integral transforms, spectral representation and the Dbar problem. Proc. R. Soc. Lond. A, 456, 805.
9. FOKAS, A. S. & PINOTSIS, D. A. (n.d.) Quaternions, Evaluation of Integrals and Boundary Value Problems (preprint).
10. FOKAS, A. S. & SUNG, L. Y. (1992) On the solvability of the N-wave, Davey-Stewartson and the Kadomtsev-Petviashvili equations. Inverse Problems, 8, 673.
11. FOKAS, A. S. & SUNG, L. Y. (2005) Generalized Fourier transforms, their nonlinearization and the imaging of the brain. Notices of the AMS, 52(10), 1178.
12. FOKAS, A. S. & ZYSKIN, M. (2002) The fundamental differential form and boundary value problems. Quart. J. Mech. Appl. Math. 55(3), 457.
13. HENKIN, G. (1990) Encycl. Math. Sciences, Vol. 7, Springer-Verlag.
14. HÖRMANDER, L. (1966) An Introduction to Complex Analysis in Several Variables. D. van Nostrand.
15. KRANTZ, S. G. (1982) Functions of Several Complex Variables. Wiley.
16. MUSKHELISHVILI, N. I. (1963) Some basic problems of the mathematical theory of elasticity. Noordhoff.
17. PINOTSIS, D. A. (2006) A nonlocal form of the Dbar problem and boundary value problems in two dimensions. In: Advances in Scattering theory and Biomedical Engineering. Wiley.
18. VEKUA, I. N. (1962) Generalized Analytic Functions. Pergamon.