Geodesic
Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, pp. 551-600

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We derive an asymptotic formula of a new type for variational solutions of the Dirichlet problem for elliptic equations of arbitrary order. The only a priori assumption on the coefficients of the principal part of the equation is the smallness of the local oscillation near the point.

@article{ASNSP_2003_5_2_3_551_0,
     author = {Kozlov, Vladimir and Maz'ya, Vladimir},
     title = {Asymptotic formula for solutions to the {Dirichlet} problem for elliptic equations with discontinuous coefficients near the boundary},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {551--600},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {3},
     year = {2003},
     mrnumber = {2020860},
     zbl = {1170.35340},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_3_551_0/}
}
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Kozlov, Vladimir; Maz'ya, Vladimir. Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, pp. 551-600. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_3_551_0/