Displaying similar documents to “Equilibrium shapes of charged droplets and related problems: (mostly) a review”

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

Vector variational problems and applications to optimal design

Pablo Pedregal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...

On optimal credibility premiums in multiperiod insurance

W. Antoniak, M. Kałuszka (2014)

Applicationes Mathematicae

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This paper focuses on the problem of optimal arrangement of a stream of premiums in a multiperiod credibility model. On the basis of a given claim history (screening) and some individual information unknown to the insurance company (signaling), we derive the optimal streams in the case when the coverage period is not necessarily fixed, e.g., because of lapses, renewals, deaths, total losses, etc.

An equilibrium model for electricity auctions

Juri Hinz (2003)

Applicationes Mathematicae

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This work discusses the process of price formation for electrical energy within an auction-like trading environment. Calculating optimal bid strategies of power producers by equilibrium arguments, we obtain the corresponding electricity price and estimate its tail behavior.

Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

Eric Bonnetier, Richard S. Falk, Michael A. Grinfeld (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a...

Optimal streams of premiums in multiperiod credibility models

L. Gajek, P. Miś, J. Słowińska (2007)

Applicationes Mathematicae

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Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period...