Regularity Results and Parametrices of Semi-linear Boundary Problems of Product Type

Jon Johnsen ()
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Jon Johnsen: Aalborg University, Department of Mathematical Sciences

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 353-360 from Springer

Abstract: Abstract This study focuses on semi-linear problems of the form (1) $$Au + N(u) = f\;in\;\Omega $$ $$Tu = \phi \;on\;\Gamma : = \partial \Omega.$$ Here (f, ϕ) are the given data, and u the unknown. Problem (1) should be elliptic in some bounded, C∞-smooth region $$\Omega \subset \mathbb{R}^n ;$$ nthat is A should be a linear differential operator in Ω while T should be a trace operator such that the system {A, T} is elliptic in a More generally, A could be suitably “pseudo-differential” as long as {A, T} is injectively elliptic in the Boutet de Monvel calculus of boundary problems.

Date: 2003
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DOI: 10.1007/978-3-0348-8035-0_24

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