6533b85bfe1ef96bd12bbeb1

RESEARCH PRODUCT

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

Jesús Ildefonso Díaz DíazBarbara Brandolini

subject

DiscretizationMathematical analysisPerimeter symmetrizationPseudoparabolic dynamic Monge-Ampère equationThird orderOperator (computer programming)Dynamic problemSettore MAT/05 - Analisi MatematicaTwo-dimensional domainSymmetrizationOrder (group theory)AmpereConvex functionMathematics

description

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.

yearjournalcountryeditionlanguage
2017-01-01
http://hdl.handle.net/11588/662692