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://www.numdam.org/item/ASNSP_2003_5_2_3_551_0/} }

TY - JOUR AU - Kozlov, Vladimir AU - Maz'ya, Vladimir TI - Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 551 EP - 600 VL - 2 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_3_551_0/ LA - en ID - ASNSP_2003_5_2_3_551_0 ER -

%0 Journal Article %A Kozlov, Vladimir %A Maz'ya, Vladimir %T Asymptotic formula for solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients near the boundary %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 551-600 %V 2 %N 3 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2003_5_2_3_551_0/ %G en %F 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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