In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces and the modulus of continuity of the coefficients are deeply connected. This holds true in the more general framework of p-evolution equations with real characteristics where a sharp scale of Hoelder continuity, with respect to the time variable has been established. We show that, for p>1, a lack of regularity in t can be compensated by a decay as the space variable x tends to infinity
M. Cicognani, F. Colombini (2012). Modulus of continuity and decay at infinity in evolution equations with real characteristics. BASEL : Birkauser.
Modulus of continuity and decay at infinity in evolution equations with real characteristics
CICOGNANI, MASSIMO;
2012
Abstract
In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces and the modulus of continuity of the coefficients are deeply connected. This holds true in the more general framework of p-evolution equations with real characteristics where a sharp scale of Hoelder continuity, with respect to the time variable has been established. We show that, for p>1, a lack of regularity in t can be compensated by a decay as the space variable x tends to infinityFile in questo prodotto:
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