BOUNDARY ESTIMATES FOR SOLUTIONS OF TWO-PHASE OBSTACLE PROBLEMS

摘要

We establish the optimal regularity (of class W_∞~2) of a solution to the two-phase obstacle problem Δu = λ~+χ_({u > 0}) - λ~-χ_({u < 0}) in Ω, λ~± ≥ 0, λ~+ + λ~- > 0, with a nonhomogeneous Dirichlet condition in a bounded domain Ω is contained in R~n with smooth boundary approx deriv Ω.