Boundary regularity of weak solutions to nonlinear elliptic obstacle problems

M Junxia,Chu Yuming

doi:10.1155/bvp/2006/72012

Abstract

We study the boundary regularity of weak solutions to nonlinear obstacle problem with-obstacle function, and obtain the boundary regularity.

Highlights

Higher regularity of the weak solution to the p-Laplacian obstacle problem where
We consider the following variational inequality:u ∈ : A(x, ∇u) · (∇v − ∇u)dx Ω≥ H(x, u, ∇u)(v − u)dx + F(x, u) · (∇v − ∇u)dx (1.1)for all v ∈ = {v ∈ W01,p(Ω), v ≥ ψ a.e. in Ω}
We study the boundary regularity of weak solutions to nonlinear obstacle problem with C1,β-obstacle function, and obtain the Cloc1,α boundary regularity

Summary

Introduction

Higher regularity of the weak solution to the p-Laplacian obstacle problem where In the case when ψ ∈ C2(Ω), papers [4, 6, 10, 12] employed different techniques to prove interior C1,α(Ω) regularity for the solution u to (1.4). This condition is important for the existence of weak solutions to obstacle problem.

Results

Conclusion