Abstract:Let $u$ be a weak solution of a quasilinear elliptic equation of the growth $p$ with a measure right hand term $\mu $. We estimate $u(z)$ at an interior point $z$ of the domain $\Omega $, or an irregular boundary point $z\in \partial \Omega $, in terms of a norm of $u$, a nonlinear potential of $\mu $ and the Wiener integral of $\bold R^n\setminus \Omega $. This quantifies the result on necessity of the Wiener criterion.
Keywords: elliptic equations, Wiener criterion, nonlinear potentials, measure data
AMS Subject Classification: 35J67, 35J70, 35J65