Topological Optimization and Optimal Transport

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.

Contents
Part I

Geometric issues in PDE problems related to the infinity Laplace operatorSolution of free boundary problems in the presence of geometric uncertaintiesDistributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energiesHigh-order topological expansions for Helmholtz problems in 2DOn a new phase field model for the approximation of interfacial energies of multiphase systemsOptimization of eigenvalues and eigenmodes by using the adjoint methodDiscrete varifolds and surface approximation

Part II

Weak Monge–Ampere solutions of the semi-discrete optimal transportation problemOptimal transportation theory with repulsive costsWardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximationsOn the Lagrangian branched transport model and the equivalence with its Eulerian formulationOn some nonlinear evolution systems which are perturbations of Wasserstein gradient flowsPressureless Euler equations with maximal density constraint: a time-splitting schemeConvergence of a fully discrete variational scheme for a thin-film equatioInterpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance