N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences

Viscosity and Minimax Solutions for Path-Dependent Hamilton–Jacobi Equations in Infinite Dimensions and Related Differential Games

Abstract We establish new results for path-dependent Hamilton–Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar and Keller [2]. Under more general assumptions than in the cited paper (and more general than...

Generating the symmetric group by three prefix reversals

The cubic pancake graphs are Cayley graphs over the symmetric group $\mathrm{Sym}_n$ generated by three prefix reversals. There is the following open problem: characterize all the sets of three prefix reversals that generate $\mathrm{Sym}_n$. As the largest prefix reversal of len...

Optimal Extrapolation of the Derivative of a Polynomial Approximately Defined on the Lemniscate

Abstract We study the problem of optimal extrapolation (optimal recovery) of the derivative of a polynomial defined with an error on a compact set in the complex plane when the compact set is a lemniscate. Along with the extrapolation problem, we consider a related sharp inequali...