Calculus of Variations and Geometric Measure Theory

S. Delladio

Dilatations of graphs and Taylor's formula: some results about convergence

created on 05 Aug 2003
modified by delladio on 20 Jan 2006


Published Paper

Inserted: 5 aug 2003
Last Updated: 20 jan 2006

Journal: Real Anal. Exchange
Volume: 29
Number: 2
Pages: 687-712
Year: 2004


The graph of a function $f$ is subjected to non-homogeneous dilatations around the point $(x_0;f(x_0))$, related to the Taylor's expansion of $f$ at $x_0$. Some questions about convergence are considered. In particular the dilatated images of the graph are proved to behave nicely with respect to a certain varifold-like convergence. Further and stronger results are shown to hold in such a context, by suitably reinforcing the assumptions.

Keywords: Rectifiable sets, non-homogeneous blow-up, Taylor formula