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Critical sets of smooth solutions to elliptic equations in dimension 3
Let u ≡ const satisfy an elliptic equation L 0 u ≡ Σa ij D ij u + Σb j D j u = 0 with smooth coefficients in a domain in R 3 .It is shown that the critical set |∇u| -1 {0} has locally finite 1-dimensional Hausdorff measure.This …