一类非齐次A-调和方程组很弱解的性质

Quality for Very Weak Solutions to a Class of Non-Homogeneous A-harmonic Systems

该文应用 Hodge分解定理 ,得到了非齐次 A-调和方程组- Di( Aij( x,Du) ) + Difij( x) =0 ,j =1 ,… ,m的很弱解是弱解 ,进一步 ,利用 Morrey空间法与 Campanato空间法以及齐次化方法 ,作者得出了该方程的很弱解是局部 Holder连续的 ,并且得出了

Using Hodge decomposition theorem, the authors obtained that the very weak solutions to non homogeneous A harmonic systems -D\-i(A\+\{ij\}(x,Du))+D\-if\-j\+i(x)=0, j=1, \:, mare weak solutions, furthermore, using Morrey space and Campanato space method and homogenization method, the authors obtained the very weak solutions to the systems are locally Hlder continuous, and obtained the relation between the Hlder continuous exponentμ and λ.