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

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 infinity
Evolution equations of hyperbolic and Schroedinger type
53
62
M. Cicognani; F. Colombini
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/132223
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