Mingione, Giuseppe Bounds for the singular set of solutions to non linear elliptic systems. (English) Zbl 1045.35024 Calc. Var. Partial Differ. Equ. 18, No. 4, 373-400 (2003). In this paper estimates for the Hausdorff dimension of the singular set of solutions to elliptic systems \[ -\text{div }a(x,u,Du) = b(x,u,Du), \] are given. Namely, assuming the functions \(a\) and \(b\) to be Hölder continuous with respect to \((x,u)\) with exponent \(\alpha\), the Hausdorff dimension of the singular set of any weak solution is at most \(n-2\alpha\). Reviewer: Giuseppe Di Fazio (Catania) Cited in 49 Documents MSC: 35J50 Variational methods for elliptic systems 35B65 Smoothness and regularity of solutions to PDEs 35J60 Nonlinear elliptic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:elliptic systems; singular set; regularity; Hausdorff dimension; weak solution PDFBibTeX XMLCite \textit{G. Mingione}, Calc. Var. Partial Differ. Equ. 18, No. 4, 373--400 (2003; Zbl 1045.35024) Full Text: DOI