Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 462

Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals

Frank Duzaar and Klaus Steffen

We give a new proof of the small excess regularity theorems for integer multiplicity rectifiable currents of arbitrary dimension and codimension minimizing an elliptic parametric variational integral. This proof does not use indirect blow-up arguments, it covers interior and boundary regularity, it applies to almost minimizing currents, and it gives an explicit and often optimal modulus of continuity for the derivative, i.e. for the tangent plane field of the almost minimizing currents.

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