Up-to boundary regularity for a singular perturbation problem of p-Laplacian type

Abstract

In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω ⊂ Rn is a C1, α domain, f ∈ C1, α ( over(Ω, -) ) for some 0 < α < 1 and uε verifies{A formula is presented} where ε > 0, βε ( t ) = frac(1, ε) β ( frac(t, ε) ) and{A formula is presented} with some positive constants B and M, then there exists a constant C > 0 independent of ε such that {norm of matrix} ∇ uε {norm of matrix}L∞ (over(Ω, -) ) {less-than or slanted equal to} C. Show more