Iterative methods of solving quasilinear elliptic problems in domains of complicated shape. (English. Russian original) Zbl 0820.35057

Bogachev, K. Yu.

Sov. Math., Dokl. 45, No. 1, 152-156 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 322, No. 4, 641-645 (1992).

Consider the following quasilinear elliptic boundary value problem \[ \text{div} A(x,u_ 0, \nabla u_ 0) = f(x),\;x \in \Omega, \quad u_ 0(x) = 0,\;x \in \partial \Omega \tag{1} \] with appropriate growth conditions on \(A\) and domain \(\Omega\) having complicated geometry. In this note the convergence in \(W^ 1_ 2 (\Omega)\) of solutions of certain auxiliary simpler problems of the same type to the solution \(u_ 0\) of the original problem (1) is studied.

Reviewer: P.Drábek (Plzeň)

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35A35	Theoretical approximation in context of PDEs

Keywords:

quasilinear elliptic equations of second order; approximation