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We show that each constant rank operator $mathcal{A}$ admits an exact potential $mathbb{B}$ in frequency space. We use this fact to show that the notion of $mathcal{A}$-quasiconvexity can be tested against compactly supported fields. We also show that $mathcal{A}$-free Young measures are generated by sequences $mathbb{B}u_j$, modulo shifts by the barycentre.
We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential lower-semicontin
We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre bundles. We find natural algebraic and analytic conditions which give
The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schrodinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate elliptic system.
In this paper, we consider the strongly coupled nonlinear Kirchhoff-type system with vanshing potentials: [begin{cases} -left(a_1+b_1int_{mathbb{R}^3}| abla u|^2dxright)Delta u+lambda V(x)u=frac{alpha}{alpha+beta}|u|^{alpha-2}u|v|^{beta},&xinmathbb{R
We give the semiclassical asymptotic of barrier-top resonances for Schr{o}dinger operators on ${mathbb R}^{n}$, $n geq 1$, whose potential is $C^{infty}$ everywhere and analytic at infinity. In the globally analytic setting, this has already been obt