Geodesic
The elliptic problems in a family of planar open sets
Applications of Mathematics, Tome 64 (2019) no. 5, pp. 485-499.

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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.
DOI : 10.21136/AM.2019.0057-19
Classification : 35B40, 35B45, 35J25, 35J40, 35J75, 35Q99
Keywords: biharmonic operator; elliptic problems; nonsmooth boundaries; uniform singularity estimates; Sobolev spaces 
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Tami, Abdelkader. The elliptic problems in a family of planar open sets. Applications of Mathematics, Tome 64 (2019) no. 5, pp. 485-499. doi : 10.21136/AM.2019.0057-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0057-19/

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