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Displaying 61 –
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2372
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general
setting. The spaces X,Y are assumed to be polish and equipped with Borel
probability measures μ and ν. The transport cost
function c : X × Y → [0,∞] is assumed
to be Borel measurable. We show that a dual optimizer always exists, provided we interpret
it as a projective limit of certain finitely additive measures. Our methods are functional
analytic...
In this note we provide a new geometric lower bound on the so-called Grad’s number of a domain in terms of how far is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
In this note we provide a new geometric lower bound on the
so-called Grad's number of a domain Ω in terms of how far Ω
is from being axisymmetric. Such an estimate is important in the
study of the trend to equilibrium for the Boltzmann equation for
dilute gases.
The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology...
We construct a Lipschitz function f on X = ℝ ² such that, for each 0 ≠ v ∈ X, the function f is smooth on a.e. line parallel to v and f is Gâteaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dimX > 1) is an arbitrary Banach space and “a.e.” has any usual “measure sense”. This example gives an answer to a natural question concerning the author’s recent study of linearly essentially smooth functions (which generalize essentially smooth...
In this paper a model for the recovery of human and economic activities in a region, which underwent a serious disaster, is proposed. The model treats the case that the disaster region has an industrial collaboration with a non-disaster region in the production system and, especially, depends upon each other in technological development. The economic growth model is based on the classical theory of R. M. Solow (1956), and the full model is described as a nonlinear system of ordinary differential...
We prove that if f is a real valued lower semicontinuous function
on a Banach space X and if there exists a C^1, real valued Lipschitz continuous
function on X with bounded support and which is not identically equal to zero,
then f is Lipschitz continuous of constant K provided all lower subgradients of
f are bounded by K. As an application, we give a regularity result of viscosity
supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions
which satisfy a coercive condition....
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