We prove that, if the coefficients of an hyperbolic operator are Zygmund-continuous with respect to t and Lipschitz-continuous with respect to x, an energy estimate without loss of derivatives holds true. As a consequence, the Cauchy problem related to the hyperbolic operator is well-posed in Sobolev spaces.
No loss of derivatives for hyperbolic operators with Zygmund-continuous coefficients in time.
Colombini, Ferruccio;
2021-01-01
Abstract
We prove that, if the coefficients of an hyperbolic operator are Zygmund-continuous with respect to t and Lipschitz-continuous with respect to x, an energy estimate without loss of derivatives holds true. As a consequence, the Cauchy problem related to the hyperbolic operator is well-posed in Sobolev spaces.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.