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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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IMPACT FACTOR 2016: 1.182

CiteScore 2016: 0.78

SCImago Journal Rank (SJR) 2016: 1.277
Source Normalized Impact per Paper (SNIP) 2016: 0.881

Mathematical Citation Quotient (MCQ) 2016: 0.83

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1864-8266
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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

Abstract

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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Citing Articles

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[1]
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[2]
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Pacific Journal of Mathematics, 2016, Volume 281, Number 1, Page 243

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