Speaker
Shokhrukh Kholmatov
(University of Vienna)
Description
We discuss regularity properties of Cartesian minimizers of the (anisotropic) area functional
[
\int_a^b \Phi(-Du,1),dx+\int_a^b |u-g|^p,dx
]
defined on (BV(a,b)). We prove that if the (L^\infty)-norm of the forcing term (g) is sufficiently small, then every minimizer is locally Lipschitz continuous. Moreover, if the anisotropy (\Phi) is smooth and uniformly elliptic, then every minimizer is in fact of class (C^{1,1}). These results provide an anisotropic extension of a conjecture of De Giorgi concerning the regularity of Cartesian minimizers in dimension one and codimension one.
Author
Shokhrukh Kholmatov
(University of Vienna)