泛函极小与椭圆型方程组解的正则性

Regularity for Solutions to Elliptic Systems and Minima of Variational Integrals

研究定义在向量u=(u^1,…,u^N):Ω■R^n→R^N上的各项异性积分泛函F(u)=∫_Ωf(x,Du(x))dx和非线性椭圆型方程组-Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x),α=1,2,…,N.在密度函数f:Ω×R^(N×n)→R和矩阵a=(a_i~α):Ω×R^(N×n)→R^(N×n)满足某单调不等式条件下,得到u整体有界.

We deal with anisotropic integral functionals（u）=∫Ωf（x,Du（x））dxand nonlinear elliptic systems-∑ni=Di（aai（x,Du（x）））=-∑ni=1DiFai（x）,a=1,2,…,Ndefined on vector valued mappingu-（u1,…,uN）：Ω Rn→RnWe present monotonicity inequalities on the densityf：Ω×RN×n→Rand the matrix a=（aai）：Ω×RN×n→RN×n, which guarantee global bounds of u.