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p-Harmonic Functions in the Heisenberg Group: Boundary Behaviour in Domains Well-approximated by Non-characteristic Hyperplanes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 357, no 1, 307-353 p.Article in journal (Refereed) Published
Abstract [en]

n this paper we study, for given p, 1 < p < 8, the boundary behaviour of non-negative p-harmonic functions in the Heisenberg group H-n, i.e., we consider weak solutions tothe non-linear and potentially degenerate partial differential equation Sigma (2n)(i=1) Xi (vertical bar Xu vertical bar(p-2) X(i)u) = 0 where the vector fields X1, ... , X-2n form a basis for the space of left-invariant vector fields on Hn. In particular, we introduce a set of domains Omega subset of H-n which we refer to asdomains well-approximated by non-characteristic hyperplanes and in Omega we prove, for 2 <= p < infinity, the boundary Harnack inequality as well as the Holder continuity for ratios of positive p-harmonic functions vanishing on a portion of partial derivative Omega

Place, publisher, year, edition, pages
2013. Vol. 357, no 1, 307-353 p.
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URN: urn:nbn:se:uu:diva-164534DOI: 10.1007/s00208-013-0896-3ISI: 000322723400011OAI: diva2:468479
Available from: 2011-12-21 Created: 2011-12-21 Last updated: 2013-09-09Bibliographically approved

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Nyström, Kaj
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