We consider p-evolution equations, for p ≥ 2, with complex valued coefficients. We prove that a necessary condition for $H^infty$ well-posedness of the associated Cauchy problem is that the imaginary part of the coefficient of the subprincipal part (in the sense of Petrowski) satisfies a decay estimate as |x| → +∞.
A necessary condition for H∞ well-posedness of ρ-evolution equations
ASCANELLI, Alessia
;BOITI, Chiara;
2016
Abstract
We consider p-evolution equations, for p ≥ 2, with complex valued coefficients. We prove that a necessary condition for $H^infty$ well-posedness of the associated Cauchy problem is that the imaginary part of the coefficient of the subprincipal part (in the sense of Petrowski) satisfies a decay estimate as |x| → +∞.File in questo prodotto:
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