Local approximations by solutions of second-order elliptic equations and removable singularities (Q957826)

The problem of ``extension'' of weak solution for some elliptic differential operators is considered. Some sufficient and necessary conditions are given, in terms of the Hausdorff measure of the (bounded) domains where the coefficients of the given elliptic operator are considered. The main tools are a particular case of Adam's inequality and the external property of weak solution. Some generalization of previous results of \textit{E. P. Dolzhenko} [Izv. Akad. Nauk, Ser. Mat. 28, 1251--1270 (1964; Zbl 0178.13501)] are obtained.