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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Graziano Crasta and Ilaria Fragalà

1 Geometric issues in PDE problems related to the infinity Laplace operator

Graziano Crasta, Dipartimento di Matematica “G. Castelnuovo,” Univ. di Roma I – P.le A. Moro 2 –00185 Roma, Italy, crasta@mat.uniroma1.it

Ilaria Fragalà, Dipartimento di Matematica, Politecnico – Piazza Leonardo da Vinci, 32 –20133 Milano, Italy, ilaria.fragala@polimi.it

Abstract: We review some recent results related to the homogeneous Dirichlet problem for the infinity Laplace equation with a constant source in a bounded domain. We characterize the geometry of domains for which an overdetermined problem admits a viscosity solutions. An essential tool is a regularity result for viscosity solutions in convex domains, obtained by the ...

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