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arXiv · 1612.00300

Parametrices and exact paralinearisation of semi-linear boundary problems

Jon Johnsen
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Abstract

The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearisation. The parametrices give regularity properties under weak conditions; improvements in subdomains result from pseudo-locality of type $1,1$-operators. The framework encompasses a broad class of boundary problems in H\"older and $L_p$-Sobolev spaces (and also Besov and Lizorkin--Triebel spaces). The Besov analyses of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation.

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Jon Johnsen. 2016-12-01. Parametrices and exact paralinearisation of semi-linear boundary problems. https://doi.org/10.1080/03605300802289188

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