Applications of Mathematics, Vol. 64, No. 5, pp. 485-499, 2019
The elliptic problems in a family of planar open sets
Abdelkader Tami
Received March 12, 2019. Published online August 19, 2019.
Abstract: We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions decompose, puts into evidence the analogy of such decompositions with standard Taylor expansions, and gives uniform estimates with respect to the angle parameter. This last property allows the treatment of families of elliptic problems on families of open sets.
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Affiliations: Abdelkader Tami, Département de Mathématiques, Université des sciences et de la technologie d'Oran - Mohamed-Boudiaf, El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria, e-mail: abdelkader21fr@gmail.com, abdelkader.tami@univ-usto.dz
