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/
[ADN] Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math. 12 (1959), 623-727. | MR | Zbl
- - ,[Dahl] On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986) 1119-1138. | MR | Zbl
,[FJK] Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure, Ann. of Math. 119 (1984), 121-141. | MR | Zbl
- - ,[GT] “Elliptic Partial Differential Equations of Second Order", (2nd ed.), Springer, 1983. | MR | Zbl
- ,[H] “The Analysis of Linear Partial Differential Operators”, Vol. 1, Springer, 1983. | Zbl
,[Ken] Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, In: “Regional Conference Series in Mathematics", AMS, Providence, RI, 1994. | MR | Zbl
,[KM1] “Differential Equations with Operator Coefficients", (with Applications to Boundary Value Problems for Partial Differential Equations), Monographs in Mathematics, Springer-Verlag, 1999. | MR | Zbl
- ,[KM2] Boundary singularities of solutions to quasilinear elliptic equations, In: “Journées Équations aux dérivées partielles", Saint-Jean-de-Monts, 31 mai-4 juin, 1999, VII-1-VII-9. | Numdam | MR | Zbl
- ,[KM3] Boundary behavior of solutions to linear and nonlinear elliptic equations in plane convex domains, Mathematical Research Letters 8 (2001), 1-5. | MR | Zbl
- ,[KMR] “Conical singularities of solutions to elliptic equations”, Mathematical Surveys and Monographs 85 AMS, Providence, RI, 2001. | MR | Zbl
- - ,