We establish a scale-invariant version of the boundary Harnack principle for
p-harmonic functions in Euclidean
C
1,1-domains and obtain estimates for the decay rates of positive
p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates
to study the behavior of conformal Martin kernel functions and positive
p-superharmonic functions near the boundary of the domain.
Key words boundary Harnack principle -
p-harmonic - conformal Martin boundary - ball conditions
Mathematics Subject Classifications (2000) 35J65 - 35J25 - 31C45 - 31B25 - 31B05
H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S.
was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation.