The Journal of Geometric Analysis

, 4:393

Weakly monotone functions

  • Juan J. Manfredi

DOI: 10.1007/BF02921588

Cite this article as:
Manfredi, J.J. J Geom Anal (1994) 4: 393. doi:10.1007/BF02921588


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


Key Words and Phrases

Finite dilatationmonotone functions

Copyright information

© Mathematica Josephina, Inc. 1994

Authors and Affiliations

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