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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Communications in Partial Differential Equations
( Vol. 19 NO.9 / (1994))
Stable Asymptotics for Elliptic Systems on Plane Domains with Corners
Martin Costabel, Monique Dauge,
Pages. 1677-1726
Abstract We consider boundary value problems for elliptic systems in the sense of Agmon-Douglis-Nirenberg on plane domains with corners, where the domain, the coefficients of the operators and the right hand sides all depend on a parameter. We construct corner singularities in such a way that the corresponding decomposition of the solution into regular and singular parts is $mathbf ext{stable}$, i.e., the regular part and the coefficients of the singular functions depend smoothly on the parameter. the construction of these singular functions continues the paper [3] and generalizes results known for second order boundary value problems - see [4,5]
[12].
Contents Introduction
0.a Motivation
0.b Plan
0.c Outline of results
1. Parameter dependent boundary value problems
1.a General setting
1.b Localization
1.c ADN elliptic systems
1.d Uniform estimates
1.e Parameter regularity
2. Construction of stable singular functions
2.a Singularities with zero right hand side
2.b Singularities with polynomial right hand sides
2.c Singular right hand sides
3. Regularity in weighted Sobolev spaces
4. Complete asymptotics
4.a Taylor expansion of the operators
4.b Expansion of the singular functions
4.c Proof of theorem 1.3
4.d Examples
5. Structure of the stable asymptotics
5.a Radial behavior
5.b Angular behavior
6. Appendix: Stable differences and Leibniz formulas
Key words
Mathmatical Subject Classification