Isosupremic vectorial minimisation problems in $L^\infty$ with general nonlinear constraints

Friday 4 March, 12:00 – 13:00, M113

In this talk we discuss minimisation problems in $L^\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Via the method of $L^p$ approximations as $p\to \infty$, we illustrate the existence of constrained minimisers in $L^p$ for all large $p< \infty$, which in turn converge to a desired $L^\infty$ minimiser as $p\to \infty$. We further show that the special $L^\infty$ minimiser we construct solves a divergence PDE system which involves certain auxiliary measures as coefficients. This can be seen as a divergence form counterpart of the Aronsson-Euler PDE system which is associated with the $L^\infty$ constrained minimisation problem. This talk is based on joint work with Nikos Katzourakis.

Ed Clark (PhD student)