Currents carried by the subgradient graphs of semi-convex functions and applications to Hessian measure

Preprint English OPEN
Tu, Qiang; Chen, Wenyi;
(2015)
  • Subject: Mathematics - Differential Geometry

In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on a $n$-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. ... View more
  • References (21)
    21 references, page 1 of 3

    [1] G. Alberti, L. Ambrosio A geometrical approach to monotone functions in Rn, Math. Z., 230 (1999) 259-316.

    [2] G. Alberti, L. Ambrosio and P. Cannarsa, On the singularities of convex functions, Manuscripta Math., 76 (1992) 421-435.

    [3] J. Aubin and H. Frankowska, Set-valued analysis. systems and control: Foundations and applications, Birkh¨auser, Boston, Basel, 1990.

    [4] F. Clarke, Y. Ledyaev, R. Stern and P. Wolenski, Nonsmooth analysis and control theory, Springer-Verlag, New York, 1998.

    [5] A. Colesanti, A Steiner type formula for convex functions, Mathematika 44 (1997) 195-214

    [6] A. Colesanti and D. Hug, Hessian measures of semi-convex functions and applications to support measures of convex bodies, Manuscripta Math. 101 (2000) 209-238.

    [7] A. Colesanti and P. Salani, Generalized solutions of Hessian equations, Bull. Austral. Math. Soc., 56 (1997) 459-466.

    [8] H. Federer, Geometric measure theory, Springer-Verlag, New York, 1969.

    [9] M. Giaquinta, G. Modica and J. Souˇcek, Graphs of finite mass which cannot be approximated in area by smooth graphs, Manuscripta Math., 78 (1993) 259-271.

    [10] M. Giaquinta, G. Modica and J. Souˇcek, Cartesian currents in the calculus of variations, I, II, Springer-Verlag, Berlin, 1998.

  • Similar Research Results (3)
  • Metrics
Share - Bookmark