Bilinear space-time estimates for homogeneous wave equations
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 2, pp. 211-274. 
@article{ASENS_2000_4_33_2_211_0,
     author = {Foschi, Damiano and Klainerman, Sergiu},
     title = {Bilinear space-time estimates for homogeneous wave equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {211--274},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {2},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00109-9},
     mrnumber = {2001g:35145},
     zbl = {0959.35107},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)00109-9/}
}
TY  - JOUR
AU  - Foschi, Damiano
AU  - Klainerman, Sergiu
TI  - Bilinear space-time estimates for homogeneous wave equations
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2000
SP  - 211
EP  - 274
VL  - 33
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(00)00109-9/
DO  - 10.1016/s0012-9593(00)00109-9
LA  - en
ID  - ASENS_2000_4_33_2_211_0
ER  - 
%0 Journal Article
%A Foschi, Damiano
%A Klainerman, Sergiu
%T Bilinear space-time estimates for homogeneous wave equations
%J Annales scientifiques de l'École Normale Supérieure
%D 2000
%P 211-274
%V 33
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(00)00109-9/
%R 10.1016/s0012-9593(00)00109-9
%G en
%F ASENS_2000_4_33_2_211_0
Foschi, Damiano; Klainerman, Sergiu. Bilinear space-time estimates for homogeneous wave equations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 2, pp. 211-274. doi : 10.1016/s0012-9593(00)00109-9. http://www.numdam.org/articles/10.1016/s0012-9593(00)00109-9/

[1] Beals M., Bézard M., Low regularity local solutions for field equations, Comm. Partial Differential Equations 21 (1-2) (1996) 79-124. | MR | Zbl

[2] Foschi D., On a endpoint case of the Klainerman-Machedon estimates, Preprint, 1998.

[3] Ginibre J., Velo G., Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1) (1995) 50-68. | MR | Zbl

[4] Hörmander L., The Analysis of Linear Partial Differential Operators. I, 2nd ed., Springer Study Edition, Distribution Theory and Fourier Analysis, Springer, Berlin, 1990. | Zbl

[5] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR | Zbl

[6] Klainerman S., Machedon M., Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (9) (1993) 1221-1268. | MR | Zbl

[7] Klainerman S., Machedon M., On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J. 74 (1) (1994) 19-44. | MR | Zbl

[8] Klainerman S., Machedon M., Finite energy solutions of the Yang-Mills equations in ℝ3 + 1, Ann. of Math. 142 (1995) 39-119. | MR | Zbl

[9] Klainerman S., Machedon M., Smoothing estimates for null forms and applications, Duke Math. J. 81 (1) (1995) 99-133 (A celebration of John F. Nash, Jr.). | MR | Zbl

[10] Klainerman S., Machedon M., Estimates for null forms and the spaces H s , δ , Int. Math. Res. Not. 17 (1996) 853-865. | MR | Zbl

[11] Klainerman S., Machedon M., Remark on Strichartz-type inequalities, Int. Math. Res. Not. 5 (1996) 201-220. | MR | Zbl

[12] Klainerman S., Machedon M., On the optimal regularity for gauge field theories, Differential and Integral Equations 6 (1997) 1019-1030. | MR | Zbl

[13] Klainerman S., Machedon M., On the regularity properties of a model problem related to wave maps, Duke Math. J. 87 (3) (1997) 553-589. | MR | Zbl

[14] Klainerman S., Selberg S., Remark on the optimal regularity for equations of wave maps type, Comm. Partial Differential Equations 22 (5-6) (1997) 901-918. | MR | Zbl

[15] Klainerman S., Tataru D., On the optimal regularity for Yang-Mills equations in ℝ4+1, Preprint, 1998.

[16] Selberg S., Multilinear space-time estimates and applications to local existence theory for nonlinear wave equations, Ph.D. Thesis, Princeton University, 1999.

[17] Stein E.M., Harmonic Analysis : Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, 1993. | MR | Zbl

[18] Strichartz R.S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (3) (1977) 705-714. | MR | Zbl

[19] Tao T., private communication.

[20] Tao T., Vargas A., Vega L., A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (4) (1998) 967-1000. | MR | Zbl

[21] Tataru D., On global existence and scattering for the wave maps equation, Preprint, 1998.

[22] Tataru D., On the equation □u = |∇u|² in 5 + 1 dimensions, Preprint, 1999.

[23] Tomas P.A., A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975) 477-478. | MR | Zbl

[24] Wolff T., A sharp bilinear cone restriction estimate, Preprint, 1999.

Cité par Sources :