2012•Journal of Shaanxi Normal UniversityRequires access

Porosity of the free boundary in the obstacle problems

Zhihua Zhang

Abstract

The obstacle problem for p-Laplacian type equation is discussed.By defining a class of functions G(p) in a unit ball which contains the solutions to the obstacle problem,it is proved that the growth of each function in the class G(p) is p/(p-1).Then the p(p-1)-growth of each solution to the obstacle problem near the free boundary is obtained.By the exact growth of the functions in G(p),a porosity result for the free boundary of solutions to the obstacle problem is established.

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Key concepts: Obstacle, Obstacle problem, Boundary (topology), Free boundary problem, Mathematical analysis, Unit sphere, Mathematics, Ball (mathematics)