A parametrix construction for wave equations with C 1,1 coefficients
Annales de l'Institut Fourier, Volume 48 (1998) no. 3, p. 797-835

In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions n=2 and n=3.

Dans cet article nous construisons le groupe des ondes pour les équations des ondes à coefficients variables, sous l’hypothèse que les coefficients du symbole principal sont C 1,1 dans les variables spatiales, et lipschitziens dans la variable temporelle. Nous utilisons cette construction pour établir les estimations de Strichartz et Pecher pour des solutions du problème de Cauchy pour de telles équations, dans le cas où la dimension spatiale est n=2 ou n=3.

@article{AIF_1998__48_3_797_0,
     author = {Smith, Hart F.},
     title = {A parametrix construction for wave equations with $C^{1,1}$ coefficients},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {3},
     year = {1998},
     pages = {797-835},
     doi = {10.5802/aif.1640},
     zbl = {0974.35068},
     mrnumber = {99h:35119},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1998__48_3_797_0}
}
Smith, Hart F. A parametrix construction for wave equations with $C^{1,1}$ coefficients. Annales de l'Institut Fourier, Volume 48 (1998) no. 3, pp. 797-835. doi : 10.5802/aif.1640. http://www.numdam.org/item/AIF_1998__48_3_797_0/

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