Singularities in the Calculus of Variations
In these notes we discuss the regularity of minimizers of convex functionals in the calculus of variations, with a focus on the vectorial case. We first treat the theory of linear elliptic systems and give some consequences. Then we discuss important singular solutions of De Giorgi, Giusti-Miranda, and Maz’ya to linear elliptic systems, and of Sverak-Yan in the nonlinear case. At the end we discuss the parabolic theory.
KeywordsElliptic and parabolic systems Singular minimizers Blowup
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