A new approach to the existence of almost everywhere solutions of nonlinear PDEs
We discuss the existence of almost everywhere solutions of nonlinear PDE’s of first (in the scalar and vectorial cases) and second order.
On a partial differential equation involving the jacobian determinant
Implicit second order partial differential equations
Convex -invariant functions and refinements of von Neumann’s inequality
A function on which is -invariant is convex if and only if its restriction to the subspace of diagonal matrices is convex. This results from Von Neumann type inequalities and appeals, in the case where , to the notion of .
On the different notions of convexity for rotationally invariant functions
Some numerical methods for the study of the convexity notions arising in the calculus of variations
An explicit solution to a system of implicit differential equations
Calculus of variations with differential forms
We study integrals of the form , where , is continuous and is a -form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.
On the solvability of the equation div in and in
We show that the equation div has, in general, no Lipschitz (respectively ) solution if is (respectively ).
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