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Bernard Dacorogna

Related publications (23)

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The existence, regularity and uniqueness of a local diffeomorphism phi satisfying g(i)(phi) det del phi = f(i) for 1

Amer Inst Mathematical Sciences2014

The two well problem consists in finding maps u which satisfy some boundary conditions and whose gradient Du assumes values in the two wells . Here (similarly ) is the well generated by a 2 x 2 matrix A, i.e., is the set of matrices of the form RA, where R ...

Springer Basel Ag2013

Solution of the Dirichlet problem for the prescribed Jacobian equation using the Monge-Ampere equation

Bernard Dacorogna

We give an alternative proof, based on the Monge-Ampere equation, of Dacorogna and Moser's result (Dacorogna and Moser. 1990) [4] on the solvability with optimal regularity of the Dirichlet problem for the prescribed Jacobian equation. (C) 2012 Academie de ...

2012

The Two-Well Problem For Piecewise-Affine Maps

Bernard Dacorogna

In the two-well problem we look for a map u which satisfies Dirichlet boundary conditions and whose gradient Du assumes values in SO (2) A boolean OR SO (2) B = S-A boolean OR S-B, for two given invertible matrices A, B (an element of SO (2) A is of the fo ...

2012

Divisibility in Grassmann algebra

Bernard Dacorogna, Olivier Kneuss

Given a k-form f and an l-form g with 0

2011

A Global Version Of The Darboux Theorem With Optimal Regularity And Dirichlet Condition

Bernard Dacorogna, Olivier Kneuss

Let n > 2 be even; r >= 1 be an integer; 0 < alpha < 1; Omega be a bounded, connected, smooth, open set in R-n; and nu be its exterior unit normal. Let f, g is an element of C-r,C-alpha((Omega) over bar; Lambda(2)) be two symplectic forms (i.e., closed and ...

2011

A Dirichlet problem for orthogonal Hessians in two dimensions is explicitly solved, by characterizing all piecewise C-2 functions u Omega subset of R-2 -> R with orthogonal Hessian in terms of a property named "second order angle condition" as in (1 1) ...

2010

, ,

We discuss the existence of a diffeomorphism phi : R-n -> R-n such that ...

2010

Regularity And Selecting Principles For Implicit Ordinary Differential Equations

Bernard Dacorogna

Implicit Ordinary or Partial Differential Equations have been widely studied in recent times, essentially from the existence of solutions point of view. One of the main issues is to select a meaningful solution among the infinitely many ones. The most cele ...

2009

On the equation det del u = f with no sign hypothesis

Bernard Dacorogna, Olivier Kneuss

We prove existence of u is an element of C-k ((Omega) over bar ;R-n) satisfying ...

Springer-Verlag2009