Geodesic
Behavior of the generalized solutions of the Dirichlet problem for higher-order elliptic equations in the neighborhood of the boundary
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 114-125

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Making use of the method of weight functions and of energy inequalities, similar to the Saint-Venant principle, the authors obtain estimates which characterize the behavior of the generalized solutions of the Dirichlet problem for the general higher-order elliptic equation in the neighborhood of a boundary point. In the case of two independent variables one has obtained an estimate of the maximum of the modulus of the solution in the neighborhood of a boundary point. 
@article{ZNSL_1982_115_a9,
     author = {V. A. Kondrat'ev and O. A. Oleinik},
     title = {Behavior of the generalized solutions of the {Dirichlet} problem for higher-order elliptic equations in the neighborhood of the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--125},
     publisher = {mathdoc},
     volume = {115},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/}
}
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V. A. Kondrat'ev; O. A. Oleinik. Behavior of the generalized solutions of the Dirichlet problem for higher-order elliptic equations in the neighborhood of the boundary. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 114-125. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/