Null form estimates for ( 1 / 2 , 1 / 2 ) symbols and local existence for a quasilinear dirichlet-wave equation

Hart F. Smith; Christopher D. Sogge

Annales scientifiques de l'École Normale Supérieure (2000)

  • Volume: 33, Issue: 4, page 485-506
  • ISSN: 0012-9593

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Smith, Hart F., and 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 33.4 (2000): 485-506. <http://eudml.org/doc/82524>.

@article{Smith2000,
author = {Smith, Hart F., Sogge, Christopher D.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {convex obstacle problem; local in time existence result; Dirichle initial boundary value problem; exterior domain; strictly geodesically concave boundary},
language = {eng},
number = {4},
pages = {485-506},
publisher = {Elsevier},
title = {Null form estimates for $(1/2,1/2)$ symbols and local existence for a quasilinear dirichlet-wave equation},
url = {http://eudml.org/doc/82524},
volume = {33},
year = {2000},
}

TY - JOUR
AU - Smith, Hart F.
AU - Sogge, Christopher D.
TI - Null form estimates for $(1/2,1/2)$ symbols and local existence for a quasilinear dirichlet-wave equation
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2000
PB - Elsevier
VL - 33
IS - 4
SP - 485
EP - 506
LA - eng
KW - convex obstacle problem; local in time existence result; Dirichle initial boundary value problem; exterior domain; strictly geodesically concave boundary
UR - http://eudml.org/doc/82524
ER -

References

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  2. [2] KLAINERMAN S., MACHEDON M., Space-time estimates for null forms and the local existence theorem, Comm. Pure. Appl. Math. 46 (1993) 1221-1268. Zbl0803.35095MR94h:35137
  3. [3] MELROSE R., TAYLOR M., Near peak scattering and the corrected Kirchoff approximation for a convex obstacle, Adv. Math. 55 (1985) 242-315. Zbl0591.58034MR86m:35095
  4. [4] MELROSE R., TAYLOR M., The radiation pattern of a diffractive wave near the shadow boundary, Comm. Partial Differential Equations 11 (1985) 599-672. Zbl0632.35056MR87i:35109
  5. [5] Melrose R., Taylor M., Boundary problems for the wave equation with grazing and gliding rays, Manuscript. 
  6. [6] SEEGER A., SOGGE C., STEIN E.M., Regularity properties of Fourier integral operators, Ann. Math. 133 (1991) 231-251. Zbl0754.58037MR92g:35252
  7. [7] SMITH H., A parametrix construction for wave equations with C¹,¹ coefficients, Annales de l'Institut Fourier 48 (1998). Zbl0974.35068MR99h:35119
  8. [8] SMITH H., Strichartz and null form estimates for metrics of bounded curvature, Preprint. 
  9. [9] SMITH H., Wave equations with low regularity coefficients, in : Documenta Mathematica, Extra Volume ICM, II, Berlin, 1998, pp. 723-730. Zbl0909.35081MR99e:35126
  10. [10] SMITH H., SOGGE C., On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. Zbl0860.35081MR95m:35128
  11. [11] SOGGE C., On local existence for nonlinear wave equations satisfying variable coefficient null conditions, Comm. PDE 18 (1993) 1795-1821. Zbl0792.35125MR94m:35199
  12. [12] SOGGE C., Lectures on Nonlinear Wave Equations, Int. Press, 1995. Zbl1089.35500MR2000g:35153
  13. [13] ZWORSKI M., High frequency scattering by a convex obstacle, Duke Math. J. 61 (1990) 545-634. Zbl0732.35060MR92c:35070

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