Related papers: The Existence of Equilibrium Flows
General Equilibrium Theory is the benchmark of economics, especially its results concerning the efficient allocation of resources, known as the First and Second Welfare Theorems. Yet, General Equilibrium Theory is beyond the scope of most…
Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.
International trade and logistics are subject to factors including geopolitical instability, climate change, and black swan events such as the unforeseen closure of the Suez Canal. The problem of predicting local price change under…
We are interested in existence of gradient flows for shape functionals especially for first Laplacian eigenvalues. We introduce different techniques to prove existence and use different formulations for gradient flows. We apply a…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
Long waves in rivers, estuaries and floods are described by the St Venant and Boussinesq equations in classical fluid dynamics. Based on the widely used $k$-$\epsilon$ model for turbulence, we use the techniques of centre manifold theory to…
Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for…
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are…
We introduce the notions of w-lower semicontinuous and almost w-lower semicontinuous correspondence with respect to a given set and prove a new fixed-point theorem. We also introduce the notion of correspondence with e-LSCS-property. As…
The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
We present a complete characterization of the classical transfer problem for an exchange economy with an arbitrary finite number of traders. Our method is geometric, using an equilibrium manifold developed by Debreu, Mas-Colell, and…
We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential…
This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that…
This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or…
These notes discuss several topics in neoclassical economics and alternatives, with an aim of reviewing fundamental issues in modeling economic markets. I start with a brief, non-rigorous summary of the basic Arrow-Debreu model of general…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding…
We consider the class of valuations on indivisible items called gross-substitute (GS). This class was introduced by Kelso and Crawford (1982) and is widely used in studies of markets with indivisibilities. GS is a condition on the…
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that…