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manuscripta mathematica

, Volume 43, Issue 1, pp 45–72 | Cite as

An existence theorem for a non-regular variational problem

  • L. M. Sibner
Article

Abstract

A “Hodge” theorem is proved for a non-linear system of equations which are not uniformly elliptic. The solutions are p-forms which minimize a non-regular energy functional over cohomology classes. The theorem is proved by regularizing the functional and proving weak L2 existence. To obtain regularity, we first show that a scalar function of the solution is a subsolution of an elliptic equation from which it follows that the solution is bounded. Hölder continuity is then proved by comparison with a solution of a simpler system known to be Hölder continuous. The solution of the non-regular problem is then obtained from the Shiffman regularization.

Keywords

Number Theory Elliptic Equation Variational Problem Scalar Function Algebraic Geometry 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • L. M. Sibner
    • 1
  1. 1.Polytechnic Institute of New YorkBrooklynUSA

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