Sharp estimates for green potentials on non-smooth domains

Mathematical Research Letters

Volumn 11, Issue 4, 2004, Pages 481-492

  Mayboroda, Svitlana ^a   Mitrea, Marius ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Besov and Triebel Lizorkin spaces; Elliptic PDE; Green potentials; Lipschitz domains; Traces

Indexed keywords

EID: 4944258348     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2004.v11.n4.a7     Document Type: Article

References (32)

1. p-integrability of the second order derivatives of Green potentials in convex domains, Pacific J. Math., 159 (1993), 201-225.
2. p-integrability of the second order derivatives for the Neumann problem in convex domains, Indiana Univ. Math. J., 43 (1994), 1123-1138.
3. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623-727.
4. N and elliptic boundary value problems, J. Funct. Anal., 114 (1993), 286-347.
5. D.-C. Chang, S.G. Krantz and E.M. Stein, Hardy spaces and elliptic boundary value problems, The Madison Symposium on Complex Analysis (Madison, WI, 1991), 119-131, Contemp. Math., 137 Amer. Math. Soc., Providence, RI, 1992.
6. n, Trans. Amer. Math. Soc., 351 (1999), 1605-1661.
7. q-estimates for Green potentials in Lipschitz domains, Math. Scand., 44 (1979), 149-170.
8. p-Neumann problem for Laplace's equation in a Lipschitz domain, Ann. of Math., 125 (1987), 437-465.
9. E. Fabes, O. Mendez and 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.
10. J. Franke and T. Runst, Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces, Math. Nachr., 174 (1995), 113-149.
11. M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J., 34 (1985), 777-799.
12. M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, Function spaces and applications, pp. 223-246 in Lecture Notes in Math., 1302, Springer, Berlin, 1988.
13. M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal., 93 (1990), 34-170.
14. S. Fromm, Potential space estimates for Green potentials in convex domains, Proc. Amer. Math. Soc., 119 (1993), 225-233.
15. D. Goldberg, A local version of real Hardy spaces, Duke Math. J., 46 (1979), 27-42.
16. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, 24 Pitman Boston, MA, 1985.
17. P. Grisvard, G. Iooss, Problèmes aux limites unilatéraux dans des domaines non réguliers, Publications des Séminaires de Mathématiques, Université de Rennes, 9 (1975), 1-26.
18. B. Jawerth, The trace of Sobolev and Besov spaces if 0 < p < 1, Studia Math., 62 (1978), 65-71.
19. D. Jerison and C. Kenig, The functional calculus for the Laplacian on Lipschitz domains, Journés "Équations aux Dérivés Partielles," Exp. No. IV, 10 pp., École Polytech., Palaiseau, 1989.
20. D. Jerison and C. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains, J. Funct. Anal., 130 (1995), 161-219.
21. J. Johnsen, Elliptic boundary problems and the Bautet de Monvel calculus in Besov and Triebel-Lizorkin spaces, Math. Scand., 79 (1996), 25-85.
22. n, Math. Rep., 2 1984.
23. C.E. Kenig, Harmonic analysis techniques for second order elliptic boundary value problems, CBMS Regional Conference Series in Mathematics, 83 AMS, Providence, RI, 1994.
24. V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Spectral problems associated with corner singularities of solutions to elliptic equations, Mathematical Surveys and Monographs, AMS 85 2001.
25. n, Studia Math., 95 (1990), 205-228.
26. nd edition, Nauka, Moscow, 1977.
27. J. Peetre, New thoughts on Besov spaces, Duke University Mathematics Series, 1 Durham, N.C., 1976.
28. E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970.
29. 1 on manifolds and submanifolds, Canad. J. Math., 24 (1972), 915-925.
30. H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
31. H. Triebel, Theory of function spaces, Monographs in Mathematics, 78 Birkhäuser Verlag, Basel, 1983.
32. D.Z. Zanger, The inhomogeneous Neumann problem in Lipschitz domains, Comm. Partial Differential Equations, 25 (2000), 1771-1808.