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Bounds for the singular set of solutions to non linear elliptic systems. (English) Zbl 1045.35024

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 \(n-2\alpha\).

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
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