### A second order differentiability technique of Bojarski-Iwaniec in the Heisenberg group

Andràs Domokos and Juan J. Manfredi
Source: Funct. Approx. Comment. Math. Volume 40, Number 1 (2009), 69-74.

#### Abstract

We adapt a technique developed by Bojarski and Iwaniec in their celebrated 1983 paper [2] to prove second order differentiability results for $p$-harmonic functions to the case of the Heisenberg group. We prove that for $2\le p<4$ we have $X_i ( |Xu|^{(p-2)/p}\, X_j u) \in L^2_{\rm loc} (\Omega )$ and $X_i (|Xu|^p ) \in L^2_{\rm loc} (\Omega)$, where $u$ is a $p$-harmonic function in the Heisenberg group $\mathbb{H}^n$.

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Primary Subjects: 35H20, 35J70
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Permanent link to this document: http://projecteuclid.org/euclid.facm/1238418798
Zentralblatt MATH identifier: 05620885
Mathematical Reviews number (MathSciNet): MR2527629
Digital Object Identifier: doi:10.7169/facm/1238418798

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