Weakly monotone functions

  • Juan J. Manfredi


The definition of monotone function in the sense of Lebesgue is extended to the Sobolev spacesW1,p,p >n − 1. It is proven that such weakly monotone functions are continuous except in a singular set ofp-capacity zero that is empty in the casep =n. Applications to the regularity of mappings with finite dilatation appearing in nonlinear elasticity theory are given.

Math Subject Classification

35J70 30C65 

Key Words and Phrases

Finite dilatation monotone functions 


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Copyright information

© Mathematica Josephina, Inc. 1994

Authors and Affiliations

  • Juan J. Manfredi
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburgh

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