Characterization of optimal shapes and masses through Monge-Kantorovich equation

By G. Bouchitté, Giuseppe M. Buttazzo. 2001

175 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b43b0f369307f195a52c239232fdeb827e40cee0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Integral Estimates for Transport Densities (2004, background): “G. Bouchitté and G. Buttazzo, ‘Characterization of optimal shapes and masses through Monge–Kantorovich equation’, Journal European Math.”
Sharp summability for Monge Transport density via Interpolation (2004, background): “The relationship between the two problems relies on the fact that the (unique) transport density is also the unique solution of (3) (see [1,3,6]); the functions u solving (3) together with σ are also meaningful in the context of the transport problem, they are referred to as Kantorovich potentials.”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, methodology): “This kind of distance has also been used in [28] (inspired by [21]) to model free transport costs on other lower dimensional sets, and not only the boundary (with the goal to model, for instance, transportation networks, and optimize their shape).”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “In [70, 71] it is connected to some shape-optimization problems that we will not develop in this book.”
Structure of null sets in the plane and applications (2005, methodology): “(ii) The following definition of tangent bundle of a positive measure μ on R has been used in the framework of shape optimization problems (see [10], [4], and references therein): given p ∈ [1,+∞], the tangent bundle T p μ(x) is the μ-essential span of all vector-fields v ∈ L(μ) such that the (distr”
Lecture Notes on Optimal Transport Problems (2003, methodology): “The main sources for the preparation of the notes have been the papers by Bouchitt´ e–Buttazzo [13, 14 ], Caffarelli–Feldman–McCann [15], Evans–Gangbo [22], Gangbo–McCann [26], Sudakov [42] and Evans [21].”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, unknown): “On the applied side these include applications to vision (image registration and morphing [64]), economics (equilibration of supply with demand [42] [27], structure of cities [23], maximization of profits [118] [22] [49] or social welfare [49]), physics [40] [129] [95] [51], engineering (optimal sha”
THE DISTANCE FUNCTION FROM THE BOUNDARY IN A MINKOWSKI SPACE (2006, methodology): “This system of PDEs arises in problems of shape optimization (see [5]).”
Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws (2005, background): “Divergence-measure fields also arise in various other nonlinear problems such as mass transfer problems and free boundary problems (see [2, 3]).”
On the theory of divergence-measure fields and its applications (2001, methodology): “For example, see Bouchitt¶e-Buttazzo [ 4 ] for such flelds in the characterization of optimal shapes and masses through the Monge-Kantorovich equation.”
The Monge problem for strictly convex norms in Rd (2010, methodology): “The relationship between the transport density and the Monge–Kantorovich problem is given by the following formula first discovered in [10].”
Regularity properties for Monge transport density and for solutions of some shape optimization problem (2002, methodology): “In this section we will report formula (4.1),which was first introduced in [ 3 ],to write,starting from a solution γ of (1.2),a measure ν which is extremal for (1.7); the measure µ = |ν| –which is given by formula (4.2)– is called,as we said in Sect.”