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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

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Volume 9, Issue 2


Nonsolvability of the asymptotic Dirichlet problem for the p-Laplacian on Cartan–Hadamard manifolds

Ilkka Holopainen
Published Online: 2015-02-12 | DOI: https://doi.org/10.1515/acv-2014-0043


We construct, by modifying Borbély's example, a 3-dimensional Cartan–Hadamard manifold M, with sectional curvatures at most -1, such that the asymptotic Dirichlet problem for the p-Laplacian is not solvable for any p > 1.

Keywords: p-harmonic function; Dirichlet problem; Cartan–Hadamard manifold

MSC: 58J32; 53C21; 31C45

About the article

Received: 2011-10-06

Revised: 2014-10-27

Accepted: 2014-10-27

Published Online: 2015-02-12

Published in Print: 2016-04-01

Funding Source: Academy of Finland

Award identifier / Grant number: 123633

Funding Source: ESF Network HCAA

Citation Information: Advances in Calculus of Variations, Volume 9, Issue 2, Pages 163–185, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0043.

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