On properness and related properties of quasilinear systems on unbounded domains
| dc.creator | Krömer, Stefan | |
| dc.creator | Lilli, Markus | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:40:59Z | |
| dc.date.available | 2026-07-07T08:40:59Z | |
| dc.description | The purpose of this paper is to provide tools for analyzing the compactness 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. The methods presented can also be used to check Palais--Smale conditions for variational problems. | |
| dc.description | 63 pages | |
| dc.identifier | https://arxiv.org/abs/0711.0863 | |
| dc.identifier | http://arxiv.org/abs/0711.0863 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141540 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35G30, 35J55, 35A35, 49J45 | |
| dc.title | On properness and related properties of quasilinear systems on unbounded domains | |
| dc.type | text |