The boundary Harnack inequality for solutions to equations of Aronsson type in the plane

Abstract

In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain Ω ⊂ R 2 and which are solutions to a general equation of p-Laplace type, 1 < p < ∞.We also establish the same type of result for solutions to the Aronsson type equation ∇(F (x, ∇u)) • F η (x, ∇u) = 0. Concerning Ω we only assume that ∂Ω is a quasicircle.In particular, our results generalize the boundary Harnack inequalities in [BL] and [LN2] to operators with variable coefficients.

Locations

• Annales Academiae Scientiarum Fennicae Mathematica - View - PDF