Singular minimizers of strictly poly convex functional in R2x2

Bevan, Jonathan
July 2005
Calculus of Variations & Partial Differential Equations;Jul2005, Vol. 23 Issue 3, p347
Academic Journal
We give examples of non-C� one-homogeneous mappings u : B ? R� and non-negative strictly polyconvex functions f such that {Du{x) : x ? B} ? {A ? R2&3x00D7;2: f[A) = 0}, where B denotes the unit hall in R�. Such u are therefore singular minimizers of the corresponding strictly polyconvex functionals I{v) = ?B f{Dv{x)) dx in appropriate Sobolev spaces.


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