Global Compensated Compactness Theorem for General Differential Operators of First Order
Global Compensated Compactness Theorem for General Differential Operators of First Order
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DOI：
10.1007/s00205-012-0583-7
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发表时间：
2013
影响因子：
2.5
通讯作者：
H. Kozono;T. Yanagisawa
中科院分区：
文献类型：
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作者：
H. Kozono;T. Yanagisawa
设A1(x，D)和A2(x，D)是作用于光滑边界有界域上的l-向量函数的一阶微分算子。我们假设H1-范数等价于AND，其中B_i=B_i(x，ν)是由斯托克斯积分公式(ν：单位外法向)确定的与A_i(x，D)Fori=A_1，2有关的迹算子。此外，我们对A1和A2a施加了诸如AND的抵消性质，其中是Ai(i=1，2)的形式伴随微分算子。假设和分别收敛于和弱于。还假设AND被限定在其中。如果其中一个是有界的，那么它就保持这一点。我们还讨论了带边界的紧致黎曼流形上的一个相应结果。
LetA1(x,D) andA2(x,D) be differential operators of the first order acting onl-vector functionsin a bounded domainwith the smooth boundary. We assume that theH1-normis equivalent toand, whereBi=Bi(x, ν) is the trace operator ontoassociated withAi(x,D) fori= 1, 2 which is determined by the Stokes integral formula (ν: unit outer normal to). Furthermore, we impose onA1andA2a cancellation property such asand, whereis the formal adjoint differential operator ofAi(i= 1, 2). Suppose thatandconverge touandvweakly in, respectively. Assume also thatandare bounded in. If eitheroris bounded in, then it holds that. We also discuss a corresponding result on compact Riemannian manifolds with boundary.