研究定义在向量u-(u1,…,uN):Ω Rn→Rn上的各项异性积分泛函(u)=∫Ωf(x,Du(x))dx和非线性椭圆型方程组-∑ni=Di(aai(x,Du(x)))=-∑ni=1DiFai(x),a=1,2,…,N.在密度函数f:Ω×RN×n→R和矩阵a=(aai):Ω×RN×n→RN×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.