Displaying similar documents to “Interior estimates in the theory of partial differential equations and their application to initial value problems.”

The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation

Daniel Tataru (1999)

Journées équations aux dérivées partielles

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The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness...

Hölder estimates and hypoellipticity

André Unterberger, Julianne Unterberger (1976)

Annales de l'institut Fourier

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The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.