Summary: Ten Mathematical Essays on Approximation in Analysis and Topology 1
J. Ferrera, J. L�opez�G�omez, F. R. Ru��z del Portal, Editors
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2004 Elsevier B.V. All rights reserved
Maximum Principles and Principal Eigenvalues
H. Amann
Institut f�ur Mathematik, Universit�at Z�urich,
Winterthurerstr. 190, CH--8057 Z�urich, Switzerland
Abstract
In this paper well�known maximum principles are extended to second order cooperative
linear elliptic systems with cooperative boundary conditions in strong, weak, and very
weak settings. In addition, interrelations between maximum principles and principal eigen�
values are studied in detail, as well as continuity properties of principal eigenvalues under
domain perturbations.
Key words: Maximum principles, principal eigenvalues, cooperative systems, cooperative
boundary conditions, weak and very weak solutions, domain perturbations
1. Introduction
It is the main purpose of this paper to study maximum principles for linear second order
cooperative elliptic systems under general linear first order cooperative boundary condi�
tions. We are particularly interested in weak settings, in view of applications to nonlinear

Source: Amann, Herbert - Institut f�r Mathematik, Universit�t Z�rich

Collections: Mathematics