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 Hlder 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 language | English |
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Journal | Communications in Partial Differential Equations |
Volume | 33 |
Issue number | 10 |
Pages (from-to) | 1729-1787 |
Number of pages | 59 |
ISSN | 0360-5302 |
DOIs | |
Publication status | Published - 2008 |