Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains
Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains
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非光滑域中具有可测系数的椭圆系统的梯度估计
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Lihe Wang
中科院分区：
文献类型：
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作者：
Sun;Seungjin Ryu;Lihe Wang
考虑非光滑有界域上系数可测的发散型椭圆系统，求出全局W1，p, 1 < p <∞正则性的系数最小正则性要求和边界上较低水平的几何假设。在假设系数仅在一个变量中可测量，而在其他变量中具有小的BMO半范数的情况下，证明了这种W1，p正则性仍然是可用的，并且该域可以用超平面局部逼近，即超越Lipschitz范畴的δ-Reifenberg域。这种规律性很容易推广到某个Orlicz-Sobolev空间。
We consider an elliptic system in divergence form with measurable coefficients in a nonsmooth bounded domain to find a minimal regularity requirement on the coefficients and a lower level of geometric assumption on the boundary of the domain for a global W1,p, 1 < p < ∞, regularity. It is proved that such a W1,p regularity is still available under the assumption that the coefficients are merely measurable in one variable and have small BMO semi-norms in the other variables while the domain can be locally approximated by a hyperplane, a so called δ-Reifenberg domain, which is beyond the Lipschitz category. This regularity easily extends to a certain Orlicz-Sobolev space.