Geodesic
Corner Behavior of Solutions of Semilinear Dirichlet Problems
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1025-1046

Voir la notice de l'article provenant de la source Cambridge University Press

In recent years there has been considerable attention paid to the behavior of solutions of elliptic boundary value problems in domains with piecewise smooth boundary. In two dimensions the study concerns the behavior of a solution near a corner, and in three (or more) dimensions two cases have been given considerable attention: a conical vertex on the boundary, or an edge.The solution of such a problem may be singular at the nonsmooth boundary points. The standard example in two dimensions is a solution in polar coordinates of the Dirichlet problem near a corner of interior angle πα;u = r 1/α sin θ/α is a function which is harmonic in the sector 0 < θ < πα, has zero boundary values near the corner, and yet at the origin has unbounded derivatives of order > 1/α unless 1/α is an integer. 
Wigley, Neil M. Corner Behavior of Solutions of Semilinear Dirichlet Problems. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1025-1046. doi: 10.4153/CJM-1985-055-x
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