Layer potentials and Hodge decompositions in two dimensional Lipschitz domains

Mathematische Annalen

Volumn 322, Issue 1, 2002, Pages 75-101

  Mitrea, Dorina ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036002994     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080100266     Document Type: Article

References (27)

1. C. Bennett, R. Sharpley, Interpolation of Operators. Academic Press, Boston 1988
2. J. Bergh, J. Löfström, Interpolation Spaces. An Introduction. Springer, Berlin New York 1976
3. R. Brown, Z. Shen, Boundary value problems in Lipschitz cylinders for three-dimensional parabolic systems. Revista Matematica Iberoamericana 8 (1992), 271-303
4. 2 pour les courbes Lipschitziennes. Annals of Math. 116 (1982), 361-388
5. R. Coifman, G. Weiss, Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569-645
6. D. Colton, R. Kress, inverse acoustic and electromagnetic scattering theory. Appl. Math. Sci. 93. Springer, Berlin Heidelberg 1992
7. B. Dahlberg, On estimates of harmonic measure. Arch. Rat. Mech. Anal. 65 (1977), 275-288
8. p-Neumann problem for Laplace's equation in a Lipschitz domain. Ann. Math. 125 (1987), 437-465
9. p Estimates for The Three-dimensional System of Ellastostatics on Lipschitz Domains. In: Lecture Notes Pure Appl. Math., Vol. 122, 1990, pp. 621-634
10. R. Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1-4. Springer, Berlin Heidelberg 1990
11. E. Fabes, Layer potential methods for boundary value problems on Lipschitz domains. In: J. Král et al. (eds.) Potential Theory, Surveys and Problems. Springer, Lecture Notes in Math., No. 1344, 1988, pp. 55-80
12. 1 domains. Acta Math. 141 (1978), 165-186
13. E. Fabes, O. Mendez, M. Mitrea, Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains. J. Funct. Anal. 159 (1998), 323-368
14. H.G. Garnir, Les Problémes aux Limites de la Physique Mathématique. Basel, Birkhäuser 1958
15. D. Jerison, C. E. Kenig, The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. 4 (1981), 203-207
16. D. Jerison, C. E. Kenig, The Inhomogeneous Dirichlet Problem in Lipschitz Domains. J. Funct. Anal. 130 (1995), 161-219
17. N. Kalton, M. Mitrea, Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Amer. Math. Soc. 350 (1998), 3903-3922
18. C. E. Kenig, Elliptic boundary value problems on Lipschitz domains, Beijing lectures in harmonic analysis (Beijing, 1984), pp. 131-183. Ann. of Math. Stud. 12, Princeton University Press, Princeton N.J. 1986
19. C. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems. AMS Regional Conferences Series in Mathematics, Vol. 83, 1994
20. O. Mendez, M. Mitrea, The Banach envelope of Besov and Triebel-Lizorkin spaces and applications. J. Four. Anal. Appl. 6 (2000), 503-531
21. D. Mitrea, The method of layer potentials for non-smooth domains with arbitrary topology. Integral Equations and Operator Theory 29 (1997), 320-338
22. p-Hodge decompositions in two dimensional Lipschitz domains. Advances in Differential Equations (2001) (to appear)
23. D. Mitrea, M. Mitrea, M. Taylor, Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds. Memoirs of AMS, Vol. 150, No. 713, 2001
24. M. Mitrea, M. Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem. J. Funct. Anal. 176 (2000), 1-79
25. T. Runst. W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Operators. de Gruyter, Berlin New York 1996
26. G. Verchota, Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains. J. Funct. Anal. 59 (1984), 572-611
27. n), 0 < p ≤ 1. Studia Math. 74 (1982), 25-33