Boundary singularities of solutions to quasilinear elliptic equations
Journées équations aux dérivées partielles (1999), article no. 7, 9 p.

Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer, 1999.

@article{JEDP_1999____A7_0,
title = {Boundary singularities of solutions to quasilinear elliptic equations},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {7},
publisher = {Universit\'e de Nantes},
year = {1999},
language = {en},
url = {http://www.numdam.org/item/JEDP_1999____A7_0/}
}
Kozlov, Vladimir; Maz'ya, Vladimir. Boundary singularities of solutions to quasilinear elliptic equations. Journées équations aux dérivées partielles (1999), article  no. 7, 9 p. http://www.numdam.org/item/JEDP_1999____A7_0/

[KM1] Kozlov, V., Maz'Ya, V. : Differential Equations with Operator Coefficients (with Applications to Boundary Value Problems for Partial Differential Equations), Monographs in Mathematics, Springer-Verlag, 1999. | MR 2001d:34090 | Zbl 0920.35003

[KM2] Kozlov, V., Maz'Ya, V. : Comparison principles for nonlinear operator differential equations in Banach spaces, Differential Operators and Spectral Theory (M. Sh. Birman's 70th Anniversary Collection), Amer. Math. Soc. Transl., Ser. 2, 189 (1999). | MR 2001k:34107 | Zbl 0923.34057

[KM3] Kozlov, V., Maz'Ya, V. : Angle singularities of solutions to the Neumann problem for the two-dimensional Riccati's equation, Asymptotic Analysis 19 (1999), 57-79. | MR 2000e:35061 | Zbl 0931.35055

[KMR] Kozlov, V., Maz'Ya, V. and Rossmann J. : Elliptic boundary value problems in domains with point singularities, Mathematical Surveys and Monographs 52 (1997), Amer. Math. Soc. | MR 98f:35038 | Zbl 0947.35004

[W] Warschawski, S.E. : On conformal mapping of infinite strips, Trans. Amer. Math. Soc. 52 (1942), 280-335. | JFM 68.0168.01 | MR 4,9b | Zbl 0028.40303