Regularity in oscillatory nonlinear elliptic systems
Regularity in oscillatory nonlinear elliptic systems
复制标题
振荡非线性椭圆系统的规律性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Melcher
中科院分区：
文献类型：
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作者：
Jan Kristensen;C. Melcher
给出了非线性椭圆方程组振动弱解（uε）在Morrey-Sobolev空间H_1，μ中的一致界.本文的主要新奇之处在于用椭圆系统的椭圆度比对ε-一致Morrey指数μ进行了精确的定性描述。这是通过证明具有Lipschitz系数的一般非线性椭圆方程组的弱解是W2，p类（局部或全局取决于假设），其中指数p > 2与维数无关，且p − 2与椭圆率成反比。
We give uniform bounds in Morrey–Sobolev spaces H1,μ for weak solutions (uε) to oscillatory nonlinear elliptic systems. The main novelty is in the precise qualitative description of the ε-uniform Morrey exponent μ in terms of the ellipticity ratio of the elliptic systems. This is achieved by showing that weak solutions of general nonlinear elliptic systems with Lipschitz coefficients are of class W2,p (locally or globally depending on assumptions) for an exponent p > 2 that is independent of dimensions and for which p − 2 is inversely proportional to the ellipticity ratio.