The Inhomogeneous Dirichlet Problem forΔ2in Lipschitz Domains

Journal of Functional Analysis

Volumn 159, Issue 1, 1998, Pages 137-190

  Adolfsson, Vilhelm ^a   Pipher, Jill ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b BROWN UNIVERSITY   (United States)

Author keywords

Biharmonic functions, Lipschitz domains, Whitney arrays, Sobolev spaces, Besov spaces

Indexed keywords

EID: 0000436626     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3300     Document Type: Article

References (29)

1. Agmon S. Maximum theorems for solutions of higher order elliptic equations. Bull. Amer. Math. Soc. 66:1960;77-80.
2. Agmon S., Douglas A., Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, II. CPAM. 12:1959;626-727.
3. Agmon S., Hörmander L. Asymptotic properties of solutions of differential equations with simple characteristics. J. Anal. Math. 30:1976;1-38.
4. Bergh J., Löfström J. Interpolation Spaces. 1976;Springer-Verlag, Berlin/New York.
5. C. V. Coffman, J. Cohen, The Duals of Harmonic Bergman Spaces, Research Report, 89-56, Dept. of Math. Carnegie Mellon University, 1989.
6. Coifman R. R., Weiss G. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83:1977;569-645.
7. q-estimates for Green potentials in Lipschitz domains. Math. Scand. 44:1979;149-170.
8. Dahlberg B. E. J. Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain. Studia Math. 67:1980;279-314.
9. q-Neumann problem for Laplace's equation in a Lipschitz domain. Ann. Math. 125:1987;437-465.
10. Dahlberg B. E. J., Kenig C., Verchota G. The Dirichlet problem for the biharmonic equation in a Lipschitz domain. Ann. Inst. Fourier (Grenoble). 36:1986;109-135.
11. Frazier M., Jawerth B. Decomposition of Besov Spaces. Indiana Univ. Math. J. 34:1985;777-799.
12. q-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations. Duke Math. J. 51:1984;997-1016.
13. -2α Δα Duke Math. J. 75:1994;51-78.
14. Jerison D., Kenig C. The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130:1995;161-219.
15. John F. Plane Waves and Spherical Means. 1955;Interscience, New York.
16. n. Mathematical Reports 2. 1984;Harwood Academic, Reading.
17. J. Peetre, The trace of Besov Space - a Limiting Case, Report, 1975:5, Lund Institute of Technology.
18. J. Peetre, The trace of Besov Space - a Limiting Case, Report, 1975:5, Lund Institute of Technology.
19. pfor the biharmonic equation on Lipschitz domains. Amer. J. Math. 114:1992;923-972.
20. Pipher J., Verchota G. Area integral estimates for the biharmonic operator in Lipschitz domains. Trans Amer. Math. Soc. 327:1991;903-917.
21. 1. Comment. Math. Helv. 68:1993;385-414.
22. Pipher J., Verchota G. Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Ann. Math. 142:1995;1-38.
23. J. Pipher, G. Verchota, Maximum principles for the polyharmonic equation on Lipschitz domains.
24. J. C. Polking, A restriction theorem for Besov-Lipschitz spaces.
25. Rudin W. Functional Analysis. 1979;Tata McGraw-Hill, New Delhi.
26. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970.
27. Stein E. M., Weiss G. Introduction to Fourier Analysis in Euclidean Spaces. 1971;Princeton Univ. Press, Princeton.
28. 1. Indiana Math. J. 36:1987;867-895.
29. Verchota G. The Dirichlet problem for the polyharmonic equation in Lipschitz domains. Indiana Math. J. 39:1990;671-702.