A note on a theorem of Jörgens.
Well posedness in for a weakly hyperbolic second order equation
The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces
Periodic solutions for a second order partial differential equation
Perimeter on Fractal sets.
On pseudosymmetric hyperbolic systems
Small analytic solutions to nonlinear weakly hyperbolic systems
Quasi-symmetrization of hyperbolic systems and propagation of the analytic regularity
Dopo aver introdotto la nozione di quasi-simmetrizzatore per sistemi del prim'ordine debolmente iperbolici, si dimostra che ad ogni sistema di tipo Sylvester, cioè proveniente da un'equazione scalare di ordine superiore, si può associare in modo regolare un quasi-simmetrizzatore. Come applicazione di questo risultato si prova che, per qualunque sistema semi-lineare debolmente iperbolico, le soluzioni Gevrey in x di ordine restano analitiche non appena lo siano all'istante iniziale.
On Lipschitz continuity of the solution map for two-dimensional wave maps
On a weakly hyperbolic quasilinear mixed problem of second order
Extension of CR functions to «wedge type» domains
Let be a complex manifold, a generic submanifold of , the real underlying manifold to . Let be an open subset of with analytic, a complexification of . We first recall the notion of -tuboid of and of and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for to the extendability of functions on to -tuboids of . Next, if has complex dimension 2, we give results on extension...
Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
We prove almost optimal local well-posedness for the coupled Dirac–Klein–Gordon (DKG) system of equations in dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman–Machedon type. It has been known for some time that the Klein–Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.
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