Pohozaev常数的消失与奇点的可去性
Vanishing Pohozaev constant and removability of singularities
摘要：
二维变分问题的共形不变性是一个已知的条件，使爆破分析的解决方案，并推出可移除的奇点。在本文中，我们确定了另一个条件，不仅是充分的，而且是必要的，这样一个可移动的奇点。这就是波霍扎耶夫恒等式的有效性。在这种情况下，这样的身份未能举行，我们引入了一个新的数量，称为{ \it Pohozaev常数}，这一方面措施的程度Pohozaev身份失败，另一方面提供了一个表征的奇异行为的解决方案在孤立奇点。我们将其应用到具有圆锥奇点的黎曼曲面上的超刘维尔型方程的爆破分析中，因为在这种奇点的存在下，共形不变性不再成立，并且除非Pohozaev常数为零，否则局部奇点一般是不可移除的。
英文摘要：
Conformal invariance of two-dimensional variational problems is a condition known to enable a blow-up analysis of solutions and to deduce the removability of singularities. In this paper, we identify another condition that is not only sufficient, but also necessary for such a removability of singularities. This is the validity of the Pohozaev identity. In situations where such an identity fails to hold, we introduce a new quantity, called the {\it Pohozaev constant}, which on one hand measures the extent to which the Pohozaev identity fails and on the other hand provides a characterization of the singular behavior of a solution at an isolated singularity. We apply this to the blow-up analysis for super-Liouville type equations on Riemann surfaces with conical singularities, because in the presence of such singularities, conformal invariance no longer holds and a local singularity is in general non-removable unless the Pohozaev constant is vanishing.
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