障碍问题中的梯度的局部可积性(英文)

Local Integrability of Gradients in Obstacle Problems

推导二阶退化椭圆偏微分方程divA(x , u(x) ) =0的障碍问题的解的微商的局部可积性 ,此二阶退化椭圆方程需满足A(x ,ξ)·ξ≥α|ξ|p,|A(x ,ξ) |≤β(|ξ|+k(x) ) p - 1,p >1.

A local higher integrability result for the derivatives of the solutions to obstacle problems associated with the second order degenerate elliptic partial differential equation divA(x,u(x))=0 has been established where the equation satisfics conditions A(x,ξ)·ξ≥α|ξ|~p and |A(x,ξ)|≤β(|ξ|+k(x))^(p-1),p>1.