A new approach to analyticity of Dirichlet-Neumann operators

Royal Society of Edinburgh - Proceedings A

Volumn 131, Issue 4, 2001, Pages 1411-1433

  Nicholls, David P ^a   Reitich, Fernando ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044528812     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500001463     Document Type: Article

References (23)

1. G. R. Barrenechea, M. A. Barrientos and G. N. Gatica. On the numerical analysis of finite element and Dirichlet-to-Neumann methods for nonlinear exterior transmission problems. Numer. Funct. Analysis Optimiz. 19 (1998), 705-735.
2. G. R. Barrenechea, G. N. Gatica and G. C. Hsiao. Weak solvability of interior transmission problems via mixed finite elements and Dirichlet-to-Neumann mappings. J. Comput. Appl. Math. 100 (1998), 145-160.
3. O. P. Bruno and F. Reitich. Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain. Proc. R. Soc. Edinb. A 122 (1992), 317-340.
4. O. P. Bruno and F. Reitich. Numerical solution of diffraction problems: a method of variation of boundaries. J. Opt. Soc. Am. A 10 (1993), 1168-1175.
5. O. P. Bruno and F. Reitich. Numerical solution of diffraction problems: finitely conducting gratings, Padé approximants, and singularities. J. Opt. Soc. Am. A 10 (1993), 2307-2316.
6. O. P. Bruno and F. Reitich. Numerical solution of diffraction problems: doubly periodic gratings. J. Opt. Soc. Am. A 10 (1993), 2551-2562.
7. A. P. Calderón. Cauchy integrals on Lipschitz curves and related operators. Proc. Natl Acad. Sci. USA 75 (1977), 1324-1327.
8. R. Coifman and Y. Meyer. Nonlinear harmonic analysis and analytic dependence. In Pseudodifferential operators and applications, pp. 71-78 (Providence, PA: American Mathematical Society, 1985).
9. W. Craig and D. P. Nicholls. Traveling two and three dimensional capillary gravity water waves. SIAM J. Math. Analysis 32 (2000), 323-359.
10. W. Craig and D. P. Nicholls. Traveling gravity water waves in two and three dimensions. (Preprint.)
11. W. Craig and C. Sulem. Numerical simulation of gravity waves. J. Comput. Phys. 108 (1993), 73-83.
12. W. Craig, U. Schanz and C. Sulem. The modulation regime of three-dimensional water waves and the Davey-Stewartson system. Annls Inst. H. Poincaré Analyse Non Linéaire 14 (1997), 615-667.
13. D. G. Dommermuth and D. K. P. Yue. A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184 (1987), 267-288.
14. A. Friedman and F. Reitich. Symmetry-breaking bifurcation of analytic solutions to free boundary problems: an application to a model of tumor growth. Trans. Am. Math. Soc. 353 (2001), 1587-1634.
15. C. Godrèche (ed.). Solids far from equilibrium (Cambridge University Press, 1992).
16. M. J. Grote and J. B. Keller. Nonreflecting boundary conditions for Maxwell's equations. J. Comput. Phys. 139 (1998), 327-342.
17. J. B. Keller and D. Givoli. Exact nonreflecting boundary conditions. J. Comput. Phys. 82 (1989), 172-192.
18. O. A. Ladyzhenskaya and N. N. Ural'tseva. Linear and quasilinear elliptic equations (Academic, 1968).
19. H. Lamb. Hydrodynamics, 6th edn (Cambridge University Press, 1993).
20. D. P. Nicholls. Traveling water waves: spectral continuation methods with parallel implementation. J. Comput. Phys. 143 (1998), 224-240.
21. U. Schanz. On the evolution of gravity-capillary waves in three dimensions. PhD thesis, University of Toronto (1997).
22. H. Triebel. Theory of function spaces (Basel: Birkhäuser, 1983).
23. V. Zakharov. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9 (1968), 190-194.