Geodesic
Smoothness Properties of Bounded Solutions of Dirichlet's Problem for Elliptic Equations in Regions with Corners on the Boundary
Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 213-226

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We study here the smoothness of solutions of the Dirichlet problem for elliptic equations in a region G with a piece-wise smooth boundary. The smoothness of the solution given depends on the smoothness of the coefficients of the equation, the boundary, the boundary function and the values of the angles on the boundary and the values of the coefficients of the second derivatives at the corners. 
Azzam, A. Smoothness Properties of Bounded Solutions of Dirichlet's Problem for Elliptic Equations in Regions with Corners on the Boundary. Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 213-226. doi: 10.4153/CMB-1980-029-4
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     author = {Azzam, A.},
     title = {Smoothness {Properties} of {Bounded} {Solutions} of {Dirichlet's} {Problem} for {Elliptic} {Equations} in {Regions} with {Corners} on the {Boundary}},
     journal = {Canadian mathematical bulletin},
     pages = {213--226},
     year = {1980},
     volume = {23},
     number = {2},
     doi = {10.4153/CMB-1980-029-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-029-4/}
}
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