We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampère 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.

Brandolini B., Diaz J.I. (2017). Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator. In P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels (a cura di), Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs (pp. 119-149). Springer International Publishing [10.1007/978-3-319-64489-9_6].

Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator

Brandolini B.;
2017

Abstract

We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampère 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.
Settore MAT/05 - Analisi Matematica
978-3-319-64488-2
978-3-319-64489-9
Brandolini B., Diaz J.I. (2017). Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator. In P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels (a cura di), Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs (pp. 119-149). Springer International Publishing [10.1007/978-3-319-64489-9_6].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/493993
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