The Yamabe problem on Dirichlet spaces
The Yamabe problem on Dirichlet spaces
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发表时间：
2013-06
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通讯作者：
K. Akutagawa;G. Carron;R. Mazzeo
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作者：
K. Akutagawa;G. Carron;R. Mazzeo
我们继续前人的工作，研究了推广经典Yamabe问题的临界指数半线性椭圆（和次椭圆）问题。在[3]中，重点是具有“几乎光滑”结构的公制空间，分层空间提供了关键示例。这里的可解性准则是用全局Yamabe不变量与“局部Yamabe不变量”的严格不等式来表述的，它捕获了关于局部奇异结构的信息。所有这些在这里被推广到狄利克雷空间的集合，它承认Sobolev不等式并满足其他一些温和的假设。应用包括对CR - Yamabe问题的非球面部分的一种新方法。
We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an 'almost smooth' structure, with stratified spaces furnishing the key examples. The criterion for solvability there is phrased in terms of a strict inequality of the global Yamabe invariant with a 'local Yamabe invariant', which captures information about the local singular structure. All of this is generalized here to the setting of Dirichlet spaces which admit a Sobolev inequality and satisfy a few other mild hypotheses. Applications include a new approach to the nonspherical part of the CR Yamabe problem.