Asymptotic solution to the Dirichlet problem for a two‐dimensional Riccatti's type equation near a corner point

Article type: Research Article

Authors: Maz'ya, V. | Slutskiǐ, A.S.^;

Affiliations: Department of Mathematics, Linköping University, S‐58183 Linköping, Sweden | Institute of Problem of Mechanical Engineering, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russia E‐mail: [email protected]

Note: [] Corresponding author.

Abstract: The Dirichlet problem for a quasilinear elliptic equation of the second order with quadratic nonlinearity in the first derivatives is considered in a plane domain with a corner point. An asymptotic solution which has a strong singularity at this point is constructed.

Keywords: quasilinear elliptic equations, asymptotic solutions, corner boundary points

Journal: Asymptotic Analysis, vol. 39, no. 2, pp. 169-185, 2004