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arXiv · 1511.07307

The Overdetermined Cauchy Problem for $\omega$-ultradifferentiable Functions

Chiara Boiti·Elisabetta Gallucci
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Abstract

In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasianalytic weight functions $\omega$. We show that existence of solutions of the Cauchy problem is equivalent to the validity of a Phragm\'en-Lindel\"of principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties.

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Chiara Boiti, Elisabetta Gallucci. 2015-11-23. The Overdetermined Cauchy Problem for $\omega$-ultradifferentiable Functions. https://doi.org/10.1007/s00229-017-0939-2

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