We consider the class of non-negative rank-one convex isotropic integrands on R n× n
which are also positively p-homogeneous. If p≤ n= 2 we prove, conditional on the …

Abstract Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator
and other compensated compactness quantities map their natural domain of definition onto …

We study existence and regularity of solutions to the Dirichlet problem for the prescribed
Jacobian equation,\det D u= f det D u= f, where f is integrable and bounded away from zero …

We study Lipschitz critical points of the energy∫ Ω g (det D u) dx in two dimensions, where g
is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is …

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a
vectorial framework. Due to inherent topological constraints, these maps manifest a diverse …

For a nonlinear operator T satisfying certain structural assumptions, our main theorem states
that the following claims are equivalent: i) T is surjective, ii) T is open at zero, and iii) T has a …

In this dissertation, we study the problem of designing an optimal incompressible fluid flow to
achieve the most efficient heat transfer between a pair of balanced heat source and sink. We …

The present thesis addresses a broad range of weak convergence problems arising in
Nonlinear Analysis. The thesis is divided into three related but essentially independent …