We prove that, if the coefficients of an hyperbolic operator are Zygmundcontinuous 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
daniele Del Santo
Membro del Collaboration Group
;
2021-01-01
Abstract
We prove that, if the coefficients of an hyperbolic operator are Zygmundcontinuous 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:
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