C 1 , β -partial regularity of p -harmonic maps at the free boundary

Thomas Müller

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 79-107
  • ISSN: 0392-4041

Abstract

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We prove the partial C 1 , β -regolarity up to the free boundary of the p -harmonic maps which minimize the p -energy D u p d x .

How to cite

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Müller, Thomas. "$C^{1,\beta}$-partial regularity of $p$-harmonic maps at the free boundary." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 79-107. <http://eudml.org/doc/195602>.

@article{Müller2002,
abstract = {We prove the partial $C^\{1, \beta\}$-regolarity up to the free boundary of the $p$-harmonic maps which minimize the $p$-energy $\int |Du|^\{p\} \, dx$.},
author = {Müller, Thomas},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {79-107},
publisher = {Unione Matematica Italiana},
title = {$C^\{1,\beta\}$-partial regularity of $p$-harmonic maps at the free boundary},
url = {http://eudml.org/doc/195602},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Müller, Thomas
TI - $C^{1,\beta}$-partial regularity of $p$-harmonic maps at the free boundary
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 79
EP - 107
AB - We prove the partial $C^{1, \beta}$-regolarity up to the free boundary of the $p$-harmonic maps which minimize the $p$-energy $\int |Du|^{p} \, dx$.
LA - eng
UR - http://eudml.org/doc/195602
ER -

References

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  1. ALT, H. W., Lineare Funktionalanalysis, Springer, second edition 1992. Zbl0753.46001
  2. DUZAAR, F.- GASTEL, A., Minimizing p -harmonic maps at a free boundary, Boll. Unione Mat. Ital. Sez. B Artci. Ric. Mat. (8), 1 (1998), 391-406. Zbl0922.58014MR1638151
  3. FUSCO, N.- HUTCHINSON, J., Partial regularity for minimisers of certain functionals having nonquadratic growth, Ann. Mat. Pura Appl. (4), 155 (1989), 1-24. Zbl0698.49001MR1042826
  4. GIAQUINTA, M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Annals of Mathematics Studies, 105, Princeton University Press, 1983. Zbl0516.49003MR717034
  5. GIAQUINTA, M.- MODICA, G., Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math., 57 (1986), 55-99. Zbl0607.49003MR866406
  6. GILBARG, D.- TRUDINGER, N. S., Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematischen Wissenschaften224, Springer, second edition 1998. Zbl0562.35001
  7. HAMBURGER, C., Regularity of differential forms minimizing degenerate elliptic functionals, J. Reine Angew. Math., 431 (1992), 7-64. Zbl0776.35006MR1179331
  8. UHLENBECK, K., Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), 219-240. Zbl0372.35030MR474389

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