3 papers
math.AP2018
Relaxation for partially coercive integral functionals with linear growth
Filip Rindler, Giles Shaw
We prove an integral representation theorem for the -relaxation of the functional \[ \mathcal{F}\colon u\mapsto\int_Ωf(x,u(x),\nabla u(x))\;\mathrm{dd…
math.AP2018
Counterexamples in Calculus of Variations in through the vectorial Eikonal equation
Nikos Katzourakis, Giles Shaw
We show that for any regular bounded domain , , there exist infinitely many global diffeomorphisms equal to the identity on which solve…
math.AP2017
Liftings, Young measures, and lower semicontinuity
Giles Shaw, Filip Rindler
This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs for $(u_j)_j \in \mathrm{BV}(Ω;…