Boundary value problems for Dirac--type equations, with applications
Boundary value problems for Dirac--type equations, with applications
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狄拉克型方程的边值问题及其应用
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Piotr T. Chruściel
中科院分区：
文献类型：
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作者：
R. Bartnik;Piotr T. Chruściel
我们证明了一类一阶椭圆型方程组边值问题的正则性，其边界条件由谱分解确定，在系数可微性条件弱于以前已知的。我们建立了具有这些边界条件的Dirac型方程的Fredholm性质。我们的结果包括尖锐的可解性准则，在紧和非紧流形;加权Poincare和Schroedinger-Lichnerowicz不等式提供了渐近控制在非紧的情况下。一个应用产生的解决方案的维滕方程的光谱边界条件所使用的赫兹利希在他的证明几何下界的ADM质量的渐近平坦的3流形。
We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditions. Our results include sharp solvability criteria, over both compact and non-compact manifolds; weighted Poincare and Schroedinger-Lichnerowicz inequalities provide asymptotic control in the non-compact case. One application yields existence of solutions for the Witten equation with a spectral boundary condition used by Herzlich in his proof of a geometric lower bound for the ADM mass of asymptotically flat 3-manifolds.