BooksStandalone TitlesCollected Volumepp. 19–29

Relaxed energies, defect measures, and minimal currents

  • Fang-Hua Lin

    New York University, United States of America
Relaxed energies, defect measures, and minimal currents cover
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Abstract

In this chapter, we describe very briefly several earlier studies concerning energy minimizing harmonic maps and maps that minimize the so-called relaxed energy from R3R^{3} into S2S^{2}. Of particular interest is the partial regularity and properties of possible singularities of such maps. We also sketch a proof of a formula conjectured by H. Brezis and P. Mironescu (2021) concerning the relaxed kk-energy for Sobolev maps from RnR^{n} into SkS^{k}, for k>1k>1.