Geodesic
Estimates for Solutions of Wave Equations with Vanishing Curvature
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1176-1200

Voir la notice de l'article provenant de la source Cambridge University Press

The solution of the Cauchy problem for a hyperbolic partial differential equation leads to a linear combination of operators Tt of the form For example, the solution of the initial value problem is given by u(x, t) = Ttf(x) where Peral proved in [11] that Tt is bounded from LP (R n) to LP (R n) if and only if From the homogeneity, the operator norm satisfies ‖Tt ‖ ≦ Ct for all t > 0. 
Marshall, Bernard. Estimates for Solutions of Wave Equations with Vanishing Curvature. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1176-1200. doi: 10.4153/CJM-1985-064-9
@article{10_4153_CJM_1985_064_9,
     author = {Marshall, Bernard},
     title = {Estimates for {Solutions} of {Wave} {Equations} with {Vanishing} {Curvature}},
     journal = {Canadian journal of mathematics},
     pages = {1176--1200},
     year = {1985},
     volume = {37},
     number = {6},
     doi = {10.4153/CJM-1985-064-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-064-9/}
}
TY  - JOUR
AU  - Marshall, Bernard
TI  - Estimates for Solutions of Wave Equations with Vanishing Curvature
JO  - Canadian journal of mathematics
PY  - 1985
SP  - 1176
EP  - 1200
VL  - 37
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-064-9/
DO  - 10.4153/CJM-1985-064-9
ID  - 10_4153_CJM_1985_064_9
ER  - 
%0 Journal Article
%A Marshall, Bernard
%T Estimates for Solutions of Wave Equations with Vanishing Curvature
%J Canadian journal of mathematics
%D 1985
%P 1176-1200
%V 37
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-064-9/
%R 10.4153/CJM-1985-064-9
%F 10_4153_CJM_1985_064_9

[1] 1. Buchwald, V. T., Elastic waves in anisotropic media, Proc. Roy. Soc. London, Ser. A, 253 (1959), 563–580. Google Scholar

[2] 2. Courant, R. and Hilbert, D., Methods of mathematical physics. Vol. II (Interscience Publishers, New York, 1962). Google Scholar

[3] 3. Duff, G. F. D., The Cauchy problem for elastic waves in an anisotropic medium, Philos. Trans. Roy. Soc. London, Ser. A, 252 (1960), 249–273. Google Scholar

[4] 4. Greenleaf, A., Principal curvature and harmonic analysis, Indiana Math. J. 30 (1981), 519–537. Google Scholar

[5] 5. Herz, C., Fourier transforms related to convex sets, Ann. of Math. 75 (1962), 81–92. Google Scholar

[6] 6. Hlawka, E., Über Integrale auf konvexen Korpern I, Monatsh. Math. 54 (1950), 1–36; II, ibid. 54 (1950), 81–99. Google Scholar

[7] 7. Littmann, W., Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766–770. Google Scholar

[8] 8. Marshall, B., Strauss, W. and Wainger, S., Lp — Lq estimates for the Klein-Gordon equation, J. Math, pures et appl. 59 (1980), 417–440. Google Scholar

[9] 9. Marshall, B., Lp — Lq multipliers of anisotropic wave equations, Indiana Math. J. 33 (1984), 435–457. Google Scholar

[10] 10. Marshall, B., The Fourier transforms of smooth measures on hypersurfaces of Rn+1 , Can. J. Math. Google Scholar | DOI

[11] 11. Peral, J., Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114–145. Google Scholar

[12] 12. Strichartz, R. S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705–714. Google Scholar

[13] 13. Zygmund, A., Trigonometric series (Cambridge U. Press, 1959). Google Scholar

Cité par Sources :