Resolubility of ideal boundary for nonlinear Dirichlet problems. (English) Zbl 0958.31007

Maeda, Fumi-Yuki; Ono, Takayori

J. Math. Soc. Japan 52, No. 3, 561-581 (2000).

The paper deals with divergence form quasilinear elliptic differential equations of the form \[ -\text{div } A(x,\nabla u)+B(x,u)=0 \] on a domain \(\Omega\) of \({\mathbb R}^N,\) \(N\geq 2,\) where the functions \(A\) and \(B\) satisfy some natural growth conditions. By the Perron-Wiener-Brelot method, the authors show that the ideal boundary of the Royden type compactification of \(\Omega\) is resoluble with respect to the Dirichlet problem for the above equation.

Reviewer: Dian K.Palagachev (Bari)

MSC:

31C45	Other generalizations (nonlinear potential theory, etc.)
35J60	Nonlinear elliptic equations
31B20	Boundary value and inverse problems for harmonic functions in higher dimensions

Keywords:

nonlinear Dirichlet problem; resolubility of ideal boundary; Perron-Wiener-Brelot method; quasilinear elliptic equations of divergence form