Parametrices and exact paralinearization of semi-linear boundary problems

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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 paralinearization. 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 Houmllder and Lp-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.
Original languageEnglish
JournalCommunications in Partial Differential Equations
Volume33
Issue number10
Pages (from-to)1729-1787
Number of pages59
ISSN0360-5302
DOIs
Publication statusPublished - 2008

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