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}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {3}, year = {2003}, pages = {551-600}, zbl = {1170.35340}, mrnumber = {2020860}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_3_551_0} }

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, Serie 5, Volume 2 (2003) no. 3, pp. 551-600. http://www.numdam.org/item/ASNSP_2003_5_2_3_551_0/

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