Morrey-Campanato estimates for Helmholtz equations

Journal of Functional Analysis

Volumn 164, Issue 2, 1999, Pages 340-355

  Perthame, Benoit ^a   Vega, Luis ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033145381     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3391     Document Type: Article

References (16)

1. Agmon S., Hormander L. Asymptotic properties of solutions of differential equations with simple characteristics. J. Anal. Math. 30:1976;1-38.
2. Bardos C., Lebeau G., Rauch J. Scattering frequencies and Gevrey-3 singularities. Invent. Math. 90:1987;77-114.
3. J. D. Benamou, F. Castella, T. Katsaounis, B. Perthame, Helmholtz equation: Wigner transform and high frequency limit.
4. 22. Ach. Rat. Mech. Anal. 126:1994;35-58.
5. Barcelo J. A., Ruiz A., Vega L. Weighted estimates for Helmholtz equation and some applications. J. Funct. Anal. 150:1997;356-382.
6. Collin Th. Smoothing effects for dispersive equations via a generalized Wigner transform. Siam J. Math. Anal. 25:1994;1622-1641.
7. I. Gasser, P. Markowich, B. Perthame, Dispersion and moment lemmas revisited, J. Differential Equations.
8. Gerard P., Markowich P. A., Mauser N. J., Poupaud F. Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50:1997;321-357.
9. Kenig C., Ponce G., Vega L. Small solutions to nonlinear Schroedinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire. 10:1993;255-288.
10. Kenig C., Ponce G., Vega L. Smoothing effects and local existence theory for the generalized nonlinear Schroedinger equations. Invent. Math. 134:1998;489-545.
11. Lions P. L., Paul Th. Sur les mesures de Wigner. Rev. Mat. Iberoamericano. 9:1983;553-618.
12. Lions P. L., Perthame B. Lemmes de moments, de moyenne et de dispersion. C. R. Acad. Sci. Paris Sér. I Math. 314:1992;801-806.
13. Lin J. E., Strauss W. A. Decay and scattering of solutions of a nonlinear Schrödinger equation. J. Funct. Anal. 30:1978;245-263.
14. Morawetz C. S. Time decay for the nonlinear Klein-Gordon equation. Proc. Roy. Soc. London A. 306:1968;291-296.
15. Reed M., Simon B. Analysis of Operators. Methods of Modern Mathematical Physics IV. 1978;Academic Press, San Diego.
16. Zhang Bo. Radiation condition and limiting amplitude principle for acoustic propagator with two unbounded media. Proc. Roy. Soc. Edinburgh A. 128:1998;173-1992.