Quasilinear elliptic systems of second order in domains with corners and edges: Nemytskij operator, local existence and asymptotic behaviour
type: Item
instance of: scholarly article
title: Quasilinear elliptic systems of second order in domains with corners and edges: Nemytskij operator, local existence and asymptotic behaviour
zbMATH Open document ID: 1011.35048
DOI: 10.4171/ZAA/1065
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-08-12T00:00:00Z
review text: Summary: We consider systems of quasilinear partial differential equations of second order in two- and three-dimensional domains with corners and edges. The analysis is performed in weighted Sobolev spaces with attached asymptotics generated by the asymptotic behaviour of the solutions of the corresponding linearized problems near boundary singularities. Applying the local invertibility theorem in these spaces we find conditions which guarantee existence of small solutions of the nonlinear problem having the same asymptotic behaviour as the solutions of the linearized problem. The main tools are multiplication theorems and properties of composition (Nemytskij) operators in weighted Sobolev spaces. As application of the general results a steady-state drift-diffusion system is explained.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 1779536
zbMATH Keywords: quasilinear elliptic problems
zbMATH Keywords: weighted Sobolev spaces with attached asymptotics
zbMATH Keywords: asymptotic behaviour near conical points and edges
zbMATH Keywords: multiplication theorems
zbMATH Keywords: local invertibility theorem
author: Felix Ali Mehmeti
author: Marius Bochniak
author: Serge Nicaise
author: Anna-Margarete Sändig
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1779536