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The singular set of solutions to non-differentiable elliptic systems. (English) Zbl 1142.35391
Summary: We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type \[ -\text{div}\,a(x,Du) = b(x,Du). \] If the vector fields a and \(b\) are Hölder continuous with respect to the variable \(x\) with exponent \(\alpha \), then the Hausdorff dimension of the singular set of any weak solution is at most \(n - 2\alpha \).

MSC:
35J45 Systems of elliptic equations, general (MSC2000)
35A20 Analyticity in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J60 Nonlinear elliptic equations
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