Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
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DOI：
10.1016/j.jfa.2010.09.008
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发表时间：
2011
影响因子：
1.7
通讯作者：
T. Isobe
中科院分区：
文献类型：
--
作者：
T. Isobe
研究了紧致自旋流形上含临界Sobolev指数的非线性Dirac方程的一些基本分析问题。它们的解作为定义在H_（1/2）-旋量上的具有临界增长的强不定泛函的临界点而得到。当流形的维数m大于3时，我们证明了Brezis-Nirenberg型问题非平凡解的存在性。我们还证明了相关Palais-Smale序列的一个整体紧性结果和L2 mm −1-弱解的正则性。
We study some basic analytical problems for nonlinear Dirac equations involving critical Sobolev exponents on compact spin manifolds. Their solutions are obtained as critical points of certain strongly indefinite functionals defined on H1/2-spinors with critical growth. We prove the existence of a non-trivial solution for the Brezis–Nirenberg type problem when the dimension m of the manifold is larger than 3. We also prove a global compactness result for the associated Palais–Smale sequences and the regularity of L2mm−1-weak solutions.