no. 3
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.

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.

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     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},
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     url = {http://www.numdam.org/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://www.numdam.org/item/ASNSP_2003_5_2_3_551_0/

[ADN] S. Agmon - A. Douglis - L. Nirenberg, 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] B. Dahlberg, On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986) 1119-1138. | MR | Zbl

[FJK] E. Fabes - D. Jerison - C. Kenig, Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure, Ann. of Math. 119 (1984), 121-141. | MR | Zbl

[GT] D. Gilbarg - N. Trudinger, “Elliptic Partial Differential Equations of Second Order", (2nd ed.), Springer, 1983. | MR | Zbl

[H] L. Hörmander, “The Analysis of Linear Partial Differential Operators”, Vol. 1, Springer, 1983. | Zbl

[Ken] C. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, In: “Regional Conference Series in Mathematics", AMS, Providence, RI, 1994. | MR | Zbl

[KM1] V. Kozlov - V. Maz'Ya, “Differential Equations with Operator Coefficients", (with Applications to Boundary Value Problems for Partial Differential Equations), Monographs in Mathematics, Springer-Verlag, 1999. | MR | Zbl

[KM2] V. Kozlov - V. Maz'Ya, 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] V. Kozlov - V. Maz'Ya, Boundary behavior of solutions to linear and nonlinear elliptic equations in plane convex domains, Mathematical Research Letters 8 (2001), 1-5. | MR | Zbl

[KMR] V. Kozlov - V. Maz'Ya - J. Rossmann, “Conical singularities of solutions to elliptic equations”, Mathematical Surveys and Monographs 85 AMS, Providence, RI, 2001. | MR | Zbl