Calculus of Variations and Geometric Measure Theory

M. Colombo - M. Gobbino

Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow

created by colombom on 11 Mar 2011
modified on 27 May 2012


Accepted Paper

Inserted: 11 mar 2011
Last Updated: 27 may 2012

Journal: Math. Models Methods Appl. Sci.
Year: 2011


We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the general principle that ``the limit of gradient-flows is the gradient-flow of the limit''. To this end, we exploit a general result relating the Gamma-limit of a sequence of functionals to the limit of the corresponding maximal slope curves.

Keywords: Gamma-convergence, Perona-Malik equation, gradient-flow, maximal slope curves