Search results for "Quasiconvex function"
showing 7 items of 7 documents
Geometric Properties of Planar BV -Extension Domains
2009
We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.
Stackelberg equilibrium with multiple firms and setup costs
2017
Abstract I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium ex…
A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations
1996
A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconca…
Stackelberg Equilibrium with Many Leaders and Followers. The Case of Setup Costs
2016
I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium exists. Besides showi…
Approximation by uniform domains in doubling quasiconvex metric spaces
2020
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
A density problem for Sobolev spaces on Gromov hyperbolic domains
2017
We prove that for a bounded domain $\Omega\subset \mathbb R^n$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $\Omega$ is a finitely connected planar domain, the Sobolev space $W^{1,\,\infty}(\Omega)$ is dense in $W^{1,\,p}(\Omega)$ for any $1\le p<\infty$. Moreover if $\Omega$ is also Jordan or quasiconvex, then $C^{\infty}(\mathbb R^n)$ is dense in $W^{1,\,p}(\Omega)$ for $1\le p<\infty$.
Relaxation of Quasilinear Elliptic SystemsviaA-quasiconvex Envelopes
2002
We consider the weak closure WZof the set Z of all feasible pairs (solution, flow) of the family of potential elliptic systems div s0 s=1 s(x)F 0 s(ru(x )+ g(x)) f(x) =0i n; u =( u1;:::;um)2 H 1 0 (; R m ) ; =( 1;:::;s 0 )2 S; where R n is a bounded Lipschitz domain, Fs are strictly convex smooth functions with quadratic growth and S =f measurable j s(x )=0o r 1 ;s =1 ;:::;s0 ;1(x )+ +s0 (x )=1 g .W e show that WZis the zero level set for an integral functional with the integrand QF being the A-quasiconvex envelope for a certain functionF and the operator A = (curl,div) m . If the functions Fs are isotropic, then on the characteristic cone (dened by the operator A) QF coincides with the A-p…