Topological Optimization and Optimal Transport: In the Applied Sciences

Contents
Part I

• Geometric issues in PDE problems related to the infinity Laplace operator
• Solution of free boundary problems in the presence of geometric uncertainties
• Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
• High-order topological expansions for Helmholtz problems in 2D
• On a new phase field model for the approximation of interfacial energies of multiphase systems
• Optimization of eigenvalues and eigenmodes by using the adjoint method
• Discrete varifolds and surface approximation

Part II

• Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem
• Optimal transportation theory with repulsive costs
• Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
• On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
• On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
• Pressureless Euler equations with maximal density constraint: a time-splitting scheme
• Convergence of a fully discrete variational scheme for a thin-film equatio
• Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance