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.

中文翻译：

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平面开集族中的椭圆问题

我们在模型案例中提出了一种新方法来处理由 VA Kondrat'ev (1967)、P. Grisvard (1972)、(1985)、H. Blum 和 R. Rannacher (1980)、VG Maz'ya 获得的经典结果(1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami ( 2016) 和其他人，描述了可能出现在拐角附近的平面多边形域上椭圆问题的解的奇异性。它提供了对解如何分解的更精确描述，证明了这种分解与标准泰勒展开式的类比，并给出了关于角度参数的统一估计。最后一个性质允许处理开集族上的椭圆问题族。