On p-harmonic measures in half-spaces

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For all 1 < p< ∞ and N≥ 2 we prove by using ODE shooting techniques that there is a constant α(p, N) > 0 such that the p-harmonic measure in R+N of a ball of radius 0 < δ≤ 1 in RN-1 is bounded above and below by a constant times δα(p.N). We provide explicit estimates for the exponent α(p, N).




Llorente, J. G., Manfredi, J. J., Troy, W. C., & Wu, J. M. (2019). On p-harmonic measures in half-spaces. Annali Di Matematica Pura Ed Applicata, 198(4), 1381–1405. https://doi.org/10.1007/s10231-018-00822-9

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