On the regularity of the polar factorization for time dependent maps

Loeper, G.
March 2005
Calculus of Variations & Partial Differential Equations;Mar2005, Vol. 22 Issue 3, p343
Academic Journal
We consider the polar factorization of vector valued mappings, introduced in [3], in the case of a family of mappings depending on a parameter. We investigate the regularity with respect to this parameter of the terms of the polar factorization by constructing some a priori bounds. To do so, we consider the linearization of the associated Monge-Ampére equation.


Related Articles

  • The obstacle problem for Monge Ampere equation. Savin, Ovidiu // Calculus of Variations & Partial Differential Equations;Mar2005, Vol. 22 Issue 3, p303 

    We consider the following obstacle problem for Monge-Ampere equationand discuss the regularity of the free boundary. We prove thatisiffis bounded away from 0 and, and it isC1,1 if.

  • Parabolic complex Monge-Ampère type equations on closed Hermitian manifolds. Sun, Wei // Calculus of Variations & Partial Differential Equations;Dec2015, Vol. 54 Issue 4, p3715 

    We study the parabolic complex Monge-Ampère type equations on closed Hermitian manifolds. We derive uniform $$C^\infty $$ a priori estimates for normalized solutions, and then prove the $$C^\infty $$ convergence. The result also yields a way to carry out the method of continuity for elliptic...

  • MULTI-VALUED SOLUTIONS TO A CLASS OF PARABOLIC MONGE-AMPERE EQUATIONS. LIMEI DAI // Communications on Pure & Applied Analysis;May2014, Vol. 13 Issue 3, p1061 

    In this paper, we investigate the multi-valued solutions of a class of parabolic Monge-Ampère equation -ut det(D²u) = f. Using the Perron method, we obtain the existence of finitely valued and infinitely valued solutions to the parabolic Monge-Ampère equations. We generalize the results...

  • ERROR ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR THE MONGE-AMPÈRE EQUATION. AWANOU, GERARD; HENGGUANG LI // International Journal of Numerical Analysis & Modeling;2014, Vol. 11 Issue 4, p745 

    We analyze the convergence of a mixed finite element method for the elliptic Monge- Amp`ere equation in dimensions 2 and 3. The unknowns in the formulation, the scalar variable and a discrete Hessian, are approximated by Lagrange finite element spaces. The method originally proposed by Lakkis...

  • Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D. Awanou, Gerard // Calcolo;Dec2015, Vol. 52 Issue 4, p503 

    We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampère equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar variable and the Hessian matrix.

  • On a class of first order congruences of lines. De Poi, Pietro; Mezzetti, Emilia // Bulletin of the Belgian Mathematical Society - Simon Stevin;Dec2009, Vol. 16 Issue 5, p805 

    We study a class of new examples of congruences of lines of order one, i.e. the congruences associated to the completely exceptional Monge-Ampère equations. We prove that they are in general not linear, and that through a general point of the focal locus there passes a planar pencil of lines...

  • On the $$W^{2,1+\varepsilon }$$ -estimates for the Monge-Ampère equation and related real analysis. Maldonado, Diego // Calculus of Variations & Partial Differential Equations;May2014, Vol. 50 Issue 1/2, p93 

    We build upon the techniques introduced by De Philippis and Figalli regarding $$W^{2,1+\varepsilon }$$ bounds for the Monge-Ampère operator, to improve the recent $$A_\infty $$ estimates for $$\Vert D^2 \varphi \Vert $$ to $$A_2$$ ones. Also, we prove a $$(1,2)-$$ Poincaré inequality and...

  • Application of Optimal Transport Theory to Reconstruction of the Early Universe. Frisch, U.; Sobolevskiĭ1, A. // Journal of Mathematical Sciences;Mar2006, Vol. 133 Issue 4, p1539 

    The problem of deterministic reconstruction of the past kinetic history of the Universe is shown to be reduced, within the Zeldovich approximation, to solving a Monge-Ampere equation. A variational representation, due to Y. Brenier, is then employed to devise a...

  • Monge-Ampère Equations on (Para-)Kähler Manifolds: from Characteristic Subspaces to Special Lagrangian Submanifolds. Alekseevsky, Dmitri; Alonso-Blanco, Ricardo; Manno, Gianni; Pugliese, Fabrizio // Acta Applicandae Mathematica;Aug2012, Vol. 120 Issue 1, p3 

    We present the basic notions and results of the geometric theory of second order PDEs in the framework of contact and symplectic manifolds including characteristics, formal integrability, existence and uniqueness of formal solutions of non-characteristic Cauchy problems. Then, we focus our...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics