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A classification of minimal cones in \({\mathbb{R}}^ n\times {\mathbb{R}}^+\) and a counterexample to interior regularity of energy minimizing functions. (English) Zbl 0667.49030
This paper improves considerably some recent results of the author concerning the minimizing properties of the cones \[ C_ n^{\alpha}=\{0\leq x_{n+1}\leq \sqrt{\frac{\alpha}{n-1}}[x^ 2_ 1+...+x^ 2_ n]^{1/2}\}. \] It is shown that the new results are optimal. Moreover the existence of singular minimizers of class \(C^{0,}\) is established in any dimension \(n\geq 2\).
Reviewer: C.Udrişte

49Q20 Variational problems in a geometric measure-theoretic setting
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