Contribution to Book
Fully Nonlinear PDEs in Real and Complex Geometry and Optics
These lecture focus on two vector-valued extremal problems which have a common feature in that the corresponding energy functionals involve L1 norm of an energy density rather than the more familiar Lp norms. Specifically, we will address (a) the problem of extremal quasiconformal mappings and (b) the problem of absolutely minimizing Lipschitz extensions.
Capogna, L. (2014). L ∞-Extremal Mappings in AMLE and Teichmüller Theory. In E. Lanconelli & C. E. Gutierrez (Eds.), Fully Nonlinear PDEs in Real and Complex Geometry and Optics. Springer International Publishing.
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