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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

##### MSC:
 49Q20 Variational problems in a geometric measure-theoretic setting
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##### References:
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