TY - JOUR
T1 - Radial Symmetry of p-Harmonic Minimizers
AU - Koski, Aleksis
AU - Onninen, Jani
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - “It is still not known if the radial cavitating minimizers obtained by Ball (Philos Trans R Soc Lond A 306:557–611, 1982) (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy”. This quotation is from Sivaloganathan and Spector (Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201–213, 2008) and seems to be still accurate. The model case of the p-harmonic energy is considered here. We prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary. In the traction free setting, however, even the identity map need not be a global minimizer.
AB - “It is still not known if the radial cavitating minimizers obtained by Ball (Philos Trans R Soc Lond A 306:557–611, 1982) (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy”. This quotation is from Sivaloganathan and Spector (Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201–213, 2008) and seems to be still accurate. The model case of the p-harmonic energy is considered here. We prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary. In the traction free setting, however, even the identity map need not be a global minimizer.
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U2 - 10.1007/s00205-018-1246-0
DO - 10.1007/s00205-018-1246-0
M3 - Article
AN - SCOPUS:85044592440
SN - 0003-9527
VL - 230
SP - 321
EP - 342
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -