Boundary value problems for elliptic differential operators of first order
Boundary value problems for elliptic differential operators of first order
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DOI：
10.4310/sdg.2012.v17.n1.a1
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
Christian Bär;W. Ballmann
中科院分区：
文献类型：
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作者：
Christian Bär;W. Ballmann
研究一阶线性椭圆型微分算子的边值问题。基础流形可以是非紧的，但边界假设是紧的。我们要求算子的主符号沿边界沿着具有对称性。例如，狄拉克型算子就满足这一点。我们提供了一个自足的介绍（非局部）椭圆边界条件，边界正则性的解决方案，和指数理论。特别地，我们简化和推广了Dirac型算子椭圆边值问题的传统理论。我们还证明了一个相关的分解定理，Gromov和Lawson的相对指标定理和推广的协边定理的一般版本。
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.