障碍问题中梯度的全局可积性

Global Integrability of Gradients in Obstacle Problems

对于满足条件|A(x,ζ)|≤β(|ζ|+k(x))p-1及A(x,ζ).ζ≥α|ζ|p的二阶退化椭圆偏微分方程divA(x,u(x))=0,得到了障碍问题解的微商的全局高阶可积性结果.

We establish a global 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 with conditions ｜ A （ x, ξ） ｜ ≤ β（ ｜ξ｜ ＋ k （ x ） ）^ p - 1 andA （ x, ξ）·ξ≥a｜ξ｜^ P, where p 〉 1.