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On properness and related properties of quasilinear systems on unbounded domains

✍ Scribed by Stefan Krömer; Markus Lilli

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
325 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The purpose of this paper is to provide tools for analyzing the compactness properties of sequences in Sobolev spaces, in particular if the sequence gets mapped onto a compact set by some nonlinear operator. Here, our focus lies on a very general class of nonlinear operators arising in quasilinear systems of partial differential equations of second order, in divergence form. Our approach, based on a suitable decomposition lemma, admits the discussion of problems with some inherent loss of compactness, for example due to a domain with infinite measure or a lower order term with critical growth. As an application, we obtain a characterization of properness which is considerably easier to verify than the definition. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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