Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation
Smith, Hart F. ; Sogge, Christopher D.
Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000), p. 485-506 / Harvested from Numdam
@article{ASENS_2000_4_33_4_485_0,
     author = {Smith, Hart F. and Sogge, Christopher D.},
     title = {Null form estimates for $(1/2,1/2)$ symbols and local existence for a quasilinear Dirichlet-wave equation},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {33},
     year = {2000},
     pages = {485-506},
     doi = {10.1016/s0012-9593(00)00119-1},
     mrnumber = {2002j:35194},
     zbl = {01702165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2000_4_33_4_485_0}
}
Smith, Hart F.; Sogge, Christopher D. Null form estimates for $(1/2,1/2)$ symbols and local existence for a quasilinear Dirichlet-wave equation. Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000) pp. 485-506. doi : 10.1016/s0012-9593(00)00119-1. http://gdmltest.u-ga.fr/item/ASENS_2000_4_33_4_485_0/

[1] Beals M., Bezard M., Low regularity local solutions for field equations, Comm. Partial Differential Equations 21 (1996) 79-124. | MR 97e:35111 | Zbl 0852.35098

[2] Klainerman S., Machedon M., Space-time estimates for null forms and the local existence theorem, Comm. Pure. Appl. Math. 46 (1993) 1221-1268. | MR 94h:35137 | Zbl 0803.35095

[3] Melrose R., Taylor M., Near peak scattering and the corrected Kirchoff approximation for a convex obstacle, Adv. Math. 55 (1985) 242-315. | MR 86m:35095 | Zbl 0591.58034

[4] Melrose R., Taylor M., The radiation pattern of a diffractive wave near the shadow boundary, Comm. Partial Differential Equations 11 (1985) 599-672. | MR 87i:35109 | Zbl 0632.35056

[5] Melrose R., Taylor M., Boundary problems for the wave equation with grazing and gliding rays, Manuscript.

[6] Seeger A., Sogge C., Stein E.M., Regularity properties of Fourier integral operators, Ann. Math. 133 (1991) 231-251. | MR 92g:35252 | Zbl 0754.58037

[7] Smith H., A parametrix construction for wave equations with C¹,¹ coefficients, Annales de l'Institut Fourier 48 (1998). | Numdam | MR 99h:35119 | Zbl 0974.35068

[8] Smith H., Strichartz and null form estimates for metrics of bounded curvature, Preprint.

[9] Smith H., Wave equations with low regularity coefficients, in : Documenta Mathematica, Extra Volume ICM, II, Berlin, 1998, pp. 723-730. | MR 99e:35126 | Zbl 0909.35081

[10] Smith H., Sogge C., On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR 95m:35128 | Zbl 0860.35081

[11] Sogge C., On local existence for nonlinear wave equations satisfying variable coefficient null conditions, Comm. PDE 18 (1993) 1795-1821. | MR 94m:35199 | Zbl 0792.35125

[12] Sogge C., Lectures on Nonlinear Wave Equations, Int. Press, 1995. | MR 2000g:35153 | Zbl 1089.35500

[13] Zworski M., High frequency scattering by a convex obstacle, Duke Math. J. 61 (1990) 545-634. | MR 92c:35070 | Zbl 0732.35060