TY - RPRT
T1 - Parametrices and exact paralinearisation of semi-linear boundary problems
AU - Johnsen, Jon
PY - 2008
Y1 - 2008
N2 - 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 Hölder 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.
AB - 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 Hölder 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.
M3 - Report
T3 - Research Report Series
BT - Parametrices and exact paralinearisation of semi-linear boundary problems
PB - Department of Mathematical Sciences, Aalborg University
CY - Aalborg
ER -