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Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Perimeter Symmetrization of Some Dynamic and Stationary Equations Involving the Monge-Ampère Operator

Authors : Barbara Brandolini, Jesús Ildefonso Díaz

Published in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Publisher: Springer International Publishing

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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.

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previous chapter Global Well-Posedness for a Phase Transition Model with Irreversible Evolution and Acceleration Forces
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Metadata
Title
Perimeter Symmetrization of Some Dynamic and Stationary Equations Involving the Monge-Ampère Operator
Authors
Barbara Brandolini
Jesús Ildefonso Díaz
Copyright Year
2017
Book
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Print ISBN: 978-3-319-64488-2

Electronic ISBN: 978-3-319-64489-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-64489-9_6

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