On the Dirichlet problem for $p$-harmonic maps II: Targets with special structure
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- by Stefano Pigola and Giona Veronelli PDF
- Proc. Amer. Math. Soc. 144 (2016), 3173-3180 Request permission
Abstract:
In this paper we develop new geometric techniques to deal with the Dirichlet problem for a $p$-harmonic map from a compact manifold with boundary to a Cartan-Hadamard target manifold which is either $2$-dimensional or rotationally symmetric.References
- Armand Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111–122. MR 146301, DOI 10.1016/0040-9383(63)90026-0
- Mohammad Ghomi, The problem of optimal smoothing for convex functions, Proc. Amer. Math. Soc. 130 (2002), no. 8, 2255–2259. MR 1896406, DOI 10.1090/S0002-9939-02-06743-6
- Ali Fardoun and Rachid Regbaoui, Regularity and uniqueness of $p$-harmonic maps with small range, Geom. Dedicata 164 (2013), 259–271. MR 3054627, DOI 10.1007/s10711-012-9771-8
- F. T. Farrell, Lectures on surgical methods in rigidity, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1996. MR 1452860
- M. Fuchs, $p$-harmonic obstacle problems. III. Boundary regularity, Ann. Mat. Pura Appl. (4) 156 (1990), 159–180. MR 1080214, DOI 10.1007/BF01766977
- Robert Hardt and Fang-Hua Lin, Mappings minimizing the $L^p$ norm of the gradient, Comm. Pure Appl. Math. 40 (1987), no. 5, 555–588. MR 896767, DOI 10.1002/cpa.3160400503
- Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 1867354
- Stefano Pigola and Giona Veronelli, On the Dirichlet problem for $p$-harmonic maps I: compact targets, Geom. Dedicata 177 (2015), 307–322. MR 3370036, DOI 10.1007/s10711-014-9991-1
- S. Pigola, G. Veronelli, Sobolev spaces of maps and the Dirichlet problem for harmonic maps. Preprint. http://arxiv.org/abs/1412.3429
- Giona Veronelli, On $p$-harmonic maps and convex functions, Manuscripta Math. 131 (2010), no. 3-4, 537–546. MR 2592096, DOI 10.1007/s00229-010-0335-7
- Brian White, Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math. 160 (1988), no. 1-2, 1–17. MR 926523, DOI 10.1007/BF02392271
Additional Information
- Stefano Pigola
- Affiliation: Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, I-22100 Como, Italy
- MR Author ID: 701188
- Email: stefano.pigola@uninsubria.it
- Giona Veronelli
- Affiliation: Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS ( UMR 7539) 99, avenue Jean-Baptiste Clément F-93430 Villetaneuse, France
- MR Author ID: 889945
- Email: veronelli@math.univ-paris13.fr
- Received by editor(s): February 10, 2015
- Received by editor(s) in revised form: August 26, 2015
- Published electronically: March 1, 2016
- Communicated by: Guofang Wei
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3173-3180
- MSC (2010): Primary 58E20
- DOI: https://doi.org/10.1090/proc/12962
- MathSciNet review: 3487246