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, Série 4, Tome 33 (2000) no. 4, pp. 485-506.
@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},
     pages = {485--506},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {4},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00119-1},
     mrnumber = {2002j:35194},
     zbl = {01702165},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)00119-1/}
}
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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, Série 4, Tome 33 (2000) no. 4, pp. 485-506. doi : 10.1016/s0012-9593(00)00119-1. http://archive.numdam.org/articles/10.1016/s0012-9593(00)00119-1/

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[12] Sogge C., Lectures on Nonlinear Wave Equations, Int. Press, 1995. | MR | Zbl

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

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