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Dorothee FREY

Wave equations with low regularity coefficients.

In this talk we discuss fixed-time L^p estimates and Strichartz estimates for wave equations with low regularity coefficients. It was shown by Smith and Tataru that wave equations with C^{1,1} coefficients satisfy the same Strichartz estimates as the unperturbed wave equation on R^n, and that for less regular coefficients a loss of derivatives in the data occurs. We improve these results for Lipschitz coefficients with additional structural assumptions. We show that no loss of derivatives occurs at the level of fixed-time L^p estimates, and that existing Strichartz estimates can be improved. The permitted class in particular excludes singular focussing effects. We also discuss perturbation results, and a recently introduced class of function spaces adapted to Fourier integral operators.

evenements/abstract_frey.txt · Last modified: 2022/05/06 15:07 by Pierre Gilles Lemarié

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