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 ...
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 ...
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 ...
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) ...
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 ...
We exhibit explicit Lipschitz maps from R '' to R '' which have almost everywhere orthogonal gradient and are equal to zero on the boundary of a cube. We solve the problem by induction on the dimension n. (C) 2008 Elsevier Inc. All rights reserved. ...
Any finite, separately convex, positively homogeneous function on R2 is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...
