0000000000780355
AUTHOR
Jesús Ildefonso Díaz Díaz
showing 2 related works from this author
Some qualitative properties for the total variation flow
2002
We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out othe…
Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator
2017
We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampere operator as well as to the second order elliptic problem which arises after an implicit time discretization of the dynamical equation. Curiously, the dynamical problem corresponds to a third order operator but becomes a singular second order parabolic equation (involving the 3-Laplacian operator) in the class of radially symmetric convex functions. Using symmetrization techniques some quantitative comparison estimates and several qualitative properties of solutions are given.