Complex powers of the Neumann Laplacian in Lipschitz domains

Mathematische Nachrichten

Volumn 223, Issue , 2001, Pages 77-88

  Mendez, Osvaldo ^a   Mitrea, Marius ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Complex powers; Lipschitz domains; Neumann Laplacian; Sobolev spaces

Indexed keywords

EID: 0039303351     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200103)223:1<77::aid-mana77>3.0.co;2-d     Document Type: Article

References (18)

1. p - Integrability of the Second Order Derivatives for the Neumann Problem in Convex Domains, Indiana Univ. Math. J. 43 (1994), 1123-1138
2. COULHON, T., and DUONG, X. T.: Riesz Transforms for 1 ≤ p ≤ 2, to appear in Trans. of Amer. Math. Soc.
3. COWLING, M. G.: Harmonic Analysis on Semigroups, Annals of Mathematics Vol. 117 (1983), 267-283
4. q - Estimates for Green Potentials in Lipschitz Domains, Mathematica Scandinavica 44 (1979), 149-170
5. p - Boundedness of Riesz Transforms Associated with Divergence Form Operators, preprint, 1998
6. JERISON, D., and KENIG, C.: The Functional Calculus for the Laplacian on Lipschitz Domains. In: Journeés Equations aux Derivés Partielles, Saint Jean - de - Monts, Soc. Mat. de France, Ecole Polytechnique, IV.1-IV.10., Paris, 1989
7. JERISON, D., and KENIG, C.: The Inhomogeneous Dirichlet Problem in Lipschitz Domains, Journal of Functional Analysis Vol. 130 (1995), 161-219
8. FABES, E., MENDEZ, O., and MITREA, M.: Boundary Layers on Sobolev - Besov Spaces and Poisson's Equation for the Laplacian in Lipschitz Domains, J. Funct. Anal. 159 (1998), 323-368
9. KENIG, C. E.: Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, AMS CBMS Series, No. 83, 1994
10. PROTTER, H. M.: Can One Hear the Shape of a Drum? Revisited, SIAM Review Vol. 29, No. 2 (1987), 185-197
11. RUDIN, W.: Functional Analysis, McGraw - Hill, Inc., Second Edition, 1991
12. STEIN, E. M.: Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970
13. STEIN, E. M.: Topics in Harmonic Analysis Related to Littlewood - Paley Theory, Annals of Math. Studies Vol. 63, Princeton Univ. Press, Princeton, NJ, 1970
14. STEIN, E. M., and WEISS, G.: Introduction to Fourier Analysis in Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971
15. STRATILÃ, S., and ZIDÓ, L.: Lectures on Von Neumann Algebras, Ed. Academiei and Abacus Press, Bucharest/Kent, 1979
16. TRIEBEL, H.: Theory of Function Spaces, Birkhäuser, Berlin, 1983
17. VERCHOTA, G. C.: Layer Potentials and Regularity for the Dirichlet Problem for Laplace's Equation in Lipschitz Domains, Journal of Functional Analysis 59 (1984), 572-611
18. ZANGER, D.: Ph. D. Thesis, MIT, 1997