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Application of Scans and Fractional Power Integrands

  • Thierry De Pauw
  • Robert Hardt
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 59)

Abstract

In this note we describe the notion of a rectifiable scan and consider some applications [DH1], [DH2] to Plateau-type minimization problems. “Scans” were first introduced in the work [HR1] of Tristan Rivière and the second author to adequately describe certain bubbling phenomena. There, the behaviour of certain W 1,3 weakly convergent sequences of smooth maps from four-dimensional domains into S 2 led to the consideration of a necessarily infinite mass generalization of a rectifiable current. The definition of a scan is motivated by the fact that a rectifiable current can be expressed in terms of its lower-dimensional slices by oriented affine subspaces. By integral geometry, the slicing function for the rectifiable current is a mass integrable function of the subspaces. With a scan one considers more general such functions that are not necessarily mass integrable.

Keywords

Soap Film Geometric Measure Theory Rectifiable Current Interior Regularity Plateau Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Thierry De Pauw
    • 1
  • Robert Hardt
    • 2
  1. 1.Université Catholique de LouvainBelgium
  2. 2.Rice UniversityUSA

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