Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems
Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems
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DOI：
10.1007/s00229-012-0586-6
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发表时间：
2013-07
影响因子：
0.6
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
我们将希尔伯特空间上著名的拉克斯-米尔格拉姆定理推广到巴拿赫空间上。假设它是Banach空间xandy积上的连续双线性形式，其中y是自反的。如果空空间nxx和空空间nyx分别在x和y中有补，并且同时满足x和y中的某些变分不等式，则对于每一个，即对于所有的，存在至少一个这样的变分不等式，对所有的都成立。将所得结果应用于流体力学中出现的椭圆型边值问题的flr解的存在性定理。
We generalize the well-known Lax-Milgram theorem on the Hilbert space to that on the Banach space. Suppose thatis a continuous bilinear form on the productof Banach spacesXandY, whereYis reflexive. If null spacesNXandNYassociated withhave complements inXand inY, respectively, and ifsatisfies certain variational inequalities both inXand inY, then for every, i.e.,withfor all, there exists at least onesuch thatholds for allwith. We apply our result to several existence theorems ofLr-solutions to the elliptic system of boundary value problems appearing in the fluid mechanics.