Eine Bemerkung zur Hebbarkeit gewisser isolierter Singularitäten bei nichtlinearen elliptischen Systemen
We consider weak solutions \(u:\Omega\to {\mathbb{R}}^ N\) of elliptic systems \(-D_{\alpha}(a_{\alpha\beta } D_{\beta} u)=f(\cdot,u,Du)\) where f is of quadratic growth in Du. Defining the geometric dimension of an isolated singularity \(x_ 0\) of u we show that \(x_ 0\) is removable for small dimensions. So the standard smallness condition in regularity theory relating the modulus of ellipticity, the oscillation of u and the constant a in \(| f(\cdot,u,Du)|\leq a\cdot| Du|^ 2+b\) can be replaced by the condition that dim x\({}_ 0\) is sufficiently small.
scientific article; zbMATH DE number 3875821