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Volume 16, Issue 2
Harmonic Maps and Critical Points of Penalized Energy

Chunqin Zhou & Deliang Xu

J. Part. Diff. Eq., 16 (2003), pp. 111-126.

Published online: 2003-05

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  • Abstract
We discuss a sequence solutions u_ε for the E-L equations of the penalized energy defined by Chen-Struwe. We show that the blow-up set of u_ε is a H^{m-2} - rectifiable set and its weak limit satisfies a blow-up formula. Consequently, the weak limit will be a stationary harmonic map if and only if the blow-up set is stationary.
  • Keywords

Harmonic map blow-up formula penalized energy

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@Article{JPDE-16-111, author = {Chunqin Zhou and Deliang Xu }, title = {Harmonic Maps and Critical Points of Penalized Energy}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {2}, pages = {111--126}, abstract = { We discuss a sequence solutions u_ε for the E-L equations of the penalized energy defined by Chen-Struwe. We show that the blow-up set of u_ε is a H^{m-2} - rectifiable set and its weak limit satisfies a blow-up formula. Consequently, the weak limit will be a stationary harmonic map if and only if the blow-up set is stationary.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5410.html} }
TY - JOUR T1 - Harmonic Maps and Critical Points of Penalized Energy AU - Chunqin Zhou & Deliang Xu JO - Journal of Partial Differential Equations VL - 2 SP - 111 EP - 126 PY - 2003 DA - 2003/05 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5410.html KW - Harmonic map KW - blow-up formula KW - penalized energy AB - We discuss a sequence solutions u_ε for the E-L equations of the penalized energy defined by Chen-Struwe. We show that the blow-up set of u_ε is a H^{m-2} - rectifiable set and its weak limit satisfies a blow-up formula. Consequently, the weak limit will be a stationary harmonic map if and only if the blow-up set is stationary.
Chunqin Zhou and Deliang Xu . (2003). Harmonic Maps and Critical Points of Penalized Energy. Journal of Partial Differential Equations. 16 (2). 111-126. doi:
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