We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone.

In this setting, we provide unique continuation results, both in terms of interior and boundary points.

The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.

中文翻译：

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非零Neumann边界条件下圆锥体中的独特延续原理

我们考虑一个具有（可能不均匀的）Neumann条件的圆锥中的椭圆方程。运算符和强制项还可以允许圆锥顶点处的非Lipschitz奇点。

在这种情况下，我们在内部和边界点方面都提供了独特的延续结果。

证明依赖于带有余数的合适的Almgren型频率公式。作为副产品，我们获得了爆炸极限的分类结果。