×

zbMATH — the first resource for mathematics

Stable asymptotics for elliptic systems on plane domains with corners. (English) Zbl 0814.35024
Linear elliptic systems in the sense of Agmon-Douglis-Nirenberg are considered in plane domains with piecewise smooth boundaries. The authors prove asymptotic expansions at corner points of the boundary. The data of the problems, domain, coefficient functions, boundary conditions, are allowed to depend smoothly on a real parameter. The important point then is that the asymptotic expansions at singular parts of the boundaries also depend smoothly and in a controllable way on the parameter.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35C20 Asymptotic expansions of solutions to PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1002/cpa.3160170104 · Zbl 0123.28706 · doi:10.1002/cpa.3160170104
[2] M. Costabel, M. Dauge. Singularities in presence of plane cracks. In preparation. · Zbl 0822.35040
[3] DOI: 10.1002/mana.19931620117 · Zbl 0802.35032 · doi:10.1002/mana.19931620117
[4] Costabel, M. and Dauge, M. 1993.General edge asymptotics of solutions of second order elliptic boundary value problem I, Vol. 123A, 109–155. Edinburgh: Proc. Royal Soc. · Zbl 0791.35032
[5] Constabel, M. and Dauge, M. 1993.General edge asymptotics of solutions of second order elliptic boundary value problems II, Vol. 123A, 157–184. Edinburgh: Proc.Royal Soc. · Zbl 0791.35033
[6] Dauge M., Lecture Notes in Mathematics 1341 (1988)
[7] Grisvard P., Boundary Value Problems in Non-Smooth Domains (1985) · Zbl 0695.35060
[8] Kondarat’Ev V.A., Trans. Moscow Math. Soc. 16 pp 227– (1967)
[9] Lions J.L., Problèmes aux limites non homogènes et applications (1968) · Zbl 0235.65074
[10] Maz’ya V.G, Amer.Math.Soc.Transl. 123 pp 1– (1984)
[11] DOI: 10.1002/mana.19921550115 · Zbl 0794.35039 · doi:10.1002/mana.19921550115
[12] M. Costabel, M. Dauge. Singularities in presence of plane cracks. In preparation. B. Schmutzler. About the structure of branching asympotics for elliptic boundary value problems in domains with edges. In B.W. Schulze, H. Triebel, editors, Symposium ”Analysis in Domains and on Manifolds with Singularities”, Breitenbrunn 1990, Teubner-Texte zur Mathematik, Vol. 131, pages 201-207. B.G. Teubner, Leipzig 1992.
[13] DOI: 10.1007/BF01199307 · Zbl 0671.58040 · doi:10.1007/BF01199307
[14] Schulze B.W., Studies in Mathematics and its Applications 24 (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.