Article ID Journal Published Year Pages File Type
839422 Nonlinear Analysis: Theory, Methods & Applications 2015 19 Pages PDF
Abstract

In this paper we study a measure, μˆ, associated with a positive pp harmonic function uˆ defined in an open set O⊂RnO⊂Rn and vanishing on a portion ΓΓ of ∂O∂O. If p>np>n we show μˆ is concentrated on a set of σσ finite Hn−1Hn−1 measure while if p=np=n the same conclusion holds provided ΓΓ is uniformly fat in the sense of nn capacity. Our work nearly answers in the affirmative a conjecture in Lewis (2015) and also appears to be the natural extension of Jones and Wolff (1988), Wolff (1993), to higher dimensions.

Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
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