Geodesic
Asymptotic Expansion of Solutions to Elliptic Boundary Value Problems in Certain Critical Cases
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 250 (2005), pp. 54-63

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A singularly perturbed elliptic boundary value problem is considered. In a number of critical cases, an algorithm for constructing the asymptotics of a solution is described and theorems on the asymptotic expansion are proved. 
@article{TM_2005_250_a1,
     author = {S. A. Golopuz},
     title = {Asymptotic {Expansion} of {Solutions} to {Elliptic} {Boundary} {Value} {Problems} in {Certain} {Critical} {Cases}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {54--63},
     publisher = {mathdoc},
     volume = {250},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_250_a1/}
}
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S. A. Golopuz. Asymptotic Expansion of Solutions to Elliptic Boundary Value Problems in Certain Critical Cases. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 250 (2005), pp. 54-63. http://geodesic.mathdoc.fr/item/TM_2005_250_a1/