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On the Alekseev-Gr\"obner formula in Banach spaces

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arxiv 1810.10030 v1 pith:2SFFT2PY submitted 2018-10-23 math.CA

Arnulf Jentzen , Felix Lindner , Primož Pušnik This is my paper · ORCID
classification math.CA
keywords alekseev-grformulaobnerbanachodesperturbationanalysisarticle
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The Alekseev-Gr\"obner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution. In this article we provide an extension of the Alekseev-Gr\"obner formula for Banach space valued ODEs under, loosely speaking, mild conditions on the perturbation of the considered ODEs.

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  1. Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise

    math.PR 2019-08 conditional novelty 7.0 of 10

    Stochastic Burgers solutions with additive trace class noise are shown to exist uniquely in Sobolev spaces H^gamma for all gamma < min{1, 1/2+beta}.

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