Some Convexity Estimates For The Solution Of P-Laplace Equations

Elliptic partial differential equation is a class of important differetial equation.Convexity of level sets of solutions has been a topic of great interest to mathe-maticians.As one of the most important geometric property,convexity has been an issue in the study of elliptic partial differntial equation for a long time.In this paper,we study the curvature estimates of the level sets of the solution to pLaplace equation div(|?u|p-2?u)=0.By constructing an auxiliary function relating to the ?2-curvature of the level set,which satifying an differential inequality and then attaining mimimum on the bounday by maximum principle,we give the positive lower bound estimates of the ?2-curvature of the convex level sets to the solution of p-Laplace equation with Dirichlet boundary value condition on the convex ring.