On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis

Marat V. Markin

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-14

Abstract:

Given the abstract evolution equation ,   with scalar type spectral operator in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly infinite differentiable on . The important case of the equation with a normal operator in a complex Hilbert space is obtained immediately as a particular case. Also, proved is the following inherent smoothness improvement effect explaining why the case of the strong finite differentiability of the weak solutions is superfluous: if every weak solution of the equation is strongly differentiable at , then all of them are strongly infinite differentiable on .

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:4168609

DOI: 10.1155/2018/4168609

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