对角形椭圆组H^1∩L^(n(r-1)/(2-r))弱解的处处正规性

Everywhere Regularity for H^1∩L^(n(r-1)/(2-r))weak Solutions to Quasilinear Elliptic Systems in Diagonal Form

考虑对角性拟线性椭园组 -D_β(A^(αβ)(x,u)D_αu^i)=B_i(x,u,Du),x∈Ω,i=1,…,N。 (1)这里Ω是R^n中的有界域。重复上、下标α、β表示从1到n求和,D_u={D_αu^i|α=1,…

Consider the quasilinear elliptic systems in diagonal form -D_β(A^(αβ)(x,u)D_αu^i)=B_i(x,u,Du) x∈Ω?R^n,i=1,…,N As we know, under the natural growth condition, the weak solutionu of (1) is bounded, i.e. u∈H^1∩L~∞. In this paper, we weaken the bound-edness of solution u to finite integrability, i.e, u∈H^1∩L^(n(r-1)/(2-r)),1+2/n<r<2. We prive the C^(0,α) and C^(1,α) everywhere regularity for weak solutions of (1).