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Local ellipticity of F and regularity of F minimizing currents

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Part of the Lecture Notes in Mathematics book series (2803,volume 1306)

Abstract

Local convex ellipticity of a parametric integrand F at a given point in space and given tangent plane direction is defined. Using this definition, the same type of local regularity is proved for F-minimizing currents near points whose tangent planes are directions at which F is convexly elliptic, as holds for currents minimizing a globally elliptic integrand. Various notions of ellipticity are discussed. Finally, some examples are given of physically interesting parametric integrands that are only locally elliptic, and a conjecture is made as to the overall structure of surfaces minimizing the integrals of such integrands.

Keywords

  • Minimal Surface
  • Tangent Plane
  • Regularity Theorem
  • Geometric Measure Theory
  • Surface Energy Density

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.

This research was partially supported by an NSF grant

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© 1988 Springer-Verlag

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Taylor, J.E. (1988). Local ellipticity of F and regularity of F minimizing currents. In: Chern, Ss. (eds) Partial Differential Equations. Lecture Notes in Mathematics, vol 1306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082932

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  • DOI: https://doi.org/10.1007/BFb0082932

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19097-4

  • Online ISBN: 978-3-540-39107-4

  • eBook Packages: Springer Book Archive