Quasilinear Elliptic Systems of Second Order in Domains with Corners and Edges: Nemytskij Operator, Local Existence and Asymptotic Behaviour | Zendy

Félix Ali Mehmeti | Zendy; Marius Bochniak | Zendy; Serge Nicaise | Zendy; AnnaMargarete Sändig | Zendy

Open Access

Quasilinear Elliptic Systems of Second Order in Domains with Corners and Edges: Nemytskij Operator, Local Existence and Asymptotic Behaviour

Author(s) -

Félix Ali Mehmeti,

Marius Bochniak,

Serge Nicaise,

AnnaMargarete Sändig

Publication year - 2002

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1065

Subject(s) - operator (biology) , order (exchange) , mathematics , mathematical analysis , elliptic operator , pure mathematics , calculus (dental) , economics , chemistry , medicine , biochemistry , finance , repressor , transcription factor , gene , dentistry

We consider systems of quasilinear partial differential equations of second order in twoand 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.

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