一类非齐次A-调和方程组弱解的正则性

Regularity of Weak Solutions to a Class of Non-Homogeneous A-Harmonic Systems

讨论满足p(1<p≤n)次控制增长条件的散度型非齐次A-调和方程组:-Dα(Aαi(x,u,Du))+Bi(x,u,Du)=0,其中i=1,…,N,通过建立逆H lder不等式,得出该方程组弱解的局部W1,q-正则性及局部H lder连续性.

This paper studies non-homogeneous A-harmonic systems of divergence form-DαAαi(x,u,Du)+Bi(x,u,Du)=0(i=1,...,N),satisfying p(1<p≤n),power controllable growth conditions.By constructing reverse Hlder inequlity,local W1,q-regularity and Hlder continuity of the weak solutions to above systems are obtained.