Theorems on Regularity and Singularity of Energy Minimizing Maps
The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
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apply approximation arbitrary argument assume ball bounded Bp(y choose chosen claim closed collection compact complete conclude constant contained continuous converges Corollary course cover deduce defined definition denotes depending derivatives discussion energy minimizing maps equation establish estimates evidently exists fact fixed function given gives gradient hand harmonic hence Holder holds homogeneous degree zero hypothesis identity implies inequality integration ip(x j-dimensional JBp(y keeping in mind Lemma linear Lipschitz locally means measure neighbourhood notation Notice obtain operator orthogonal particular projection proof prove real-analytic Remark respect result S(ip satisfies Section 2.4 sequence shows sing singu singular smooth space subsequence subset subspace suitable Suppose tangent map Theorem unique virtue weak