The L p resolvents of elliptic operators with uniformly continuous coefficients

Journal of Differential Equations

Volumn 188, Issue 2, 2003, Pages 555-568

  Miyazaki, Yoichi ^a  

^a NIHON UNIVERSITY   (Japan)

Author keywords

Divergence form; Elliptic operator; L p theory; Non smooth coefficient; Resolvent; Uniformly continuous

Indexed keywords

EID: 0037373721     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(02)00109-2     Document Type: Article

References (26)

1. S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962) 119-147.
2. S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations, Comm. Pure Appl. Math. 12 (1959) 623-727.
3. P. Auscher, Regularity theorems and heat kernels for elliptic operators, J. London Math. Soc. 54 (1996) 284-296.
4. P. Auscher, A. McIntosh, P. Tchamitchian, Heat kernels of second order complex elliptic operators and applications, J. Funct. Anal. 152 (1998) 22-73.
5. P. Auscher, M. Qafsaoui, Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form, J. Funct. Anal. 177 (2000) 310-364.
6. 1 Domains, Lecture notes in Pure and Applied Mathematics, Vol. 215, 1998, Springer, Berlin, pp. 15-32.
7. P. Auscher, P. Tchamitchian, Square root problem for divergence operators and related topics, Astérisque 249 (1998).
8. p -perturbation of the second order coefficients, J. Differential Equations 124 (1996) 302-323.
9. G. Barbatis, Stability and regularity of higher order elliptic operators with measurable coefficients, J. London Math. Soc. 58 (1998) 342-352.
10. G. Barbatis, E.B. Davies, Sharp bounds on heat kernels of higher order uniformly elliptic operators, J. Operator Theory 36 (1996) 179-198.
11. R. Beals, Asymptotic behavior of the Green's function and spectral function of an elliptic operator, J. Funct. Anal. 5 (1970) 484-503.
12. J. Bergh, J. Löfström, Interpolation Spaces, Springer, Berlin/Heidelberg/New York, 1976.
13. E.B. Davies, Explicit constants for Gaussian upper bounds on heat kernels, Amer. J. Math. 109 (1987) 319-334.
14. E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1992.
15. E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995) 141-169.
16. p spectral theory of higher-order elliptic differential operators, Bull. London Math. Soc. 29 (1997) 513-546.
17. H. Kumano-go, Pseudo-differential Operators, MIT, Massachusetts, 1981.
18. K. Maruo, H. Tanabe, On the asymptotic distribution of eigenvalues of operators associated with strongly elliptic sesquilinear forms, Osaka J. Math. 8 (1971) 323-345.
19. Y. Miyazaki, Asymptotic behavior of spectral functions of elliptic operators with Hölder continuous coefficients, J. Math. Soc. Japan 49 (1997) 539-563.
20. p resolvents of elliptic operators with measurable coefficients and its application, in preprint.
21. T. Muramatu, On Besov spaces and Sobolev spaces of generalized functions defined on a general region, Publ. Res. Inst. Math. Sci. Kyoto Univ. 9 (1974) 325-396.
22. T. Muramatu, Theory of Interpolation Spaces and Linear Operators, Kinokuniya-Shoten, Tokyo, 1985 (in Japanese).
23. H. Tanabe, On Green's functions of elliptic and parabolic boundary value problem, Proc. Japan Acad. Ser. A 48 (1972) 709-711.
24. H. Tanabe, Functional Analysis I, II, Jikkyo Shuppan, Tokyo, 1981 (in Japanese).
25. H. Tanabe, Functional Analytic Methods for Partial Differential Equations, in: Monographs and Textbooks in Pure and Applied Mathematics, Vol. 204, Marcel Dekker, New York, 1997.
26. M.E. Taylor, Pseudodifferential Operators, Princeton University, Princeton, 1981.