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

In: Function Spaces, Differential Operators and Nonlinear Analysis

Author

Listed:
  • Jon Johnsen

    (Aalborg University, Department of Mathematical Sciences)

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.

Suggested Citation

  • Jon Johnsen, 2003. "Regularity Results and Parametrices of Semi-linear Boundary Problems of Product Type," Springer Books, in: Dorothee Haroske & Thomas Runst & Hans-Jürgen Schmeisser (ed.), Function Spaces, Differential Operators and Nonlinear Analysis, pages 353-360, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8035-0_24
    DOI: 10.1007/978-3-0348-8035-0_24
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