Related papers: The Discontinuity Problem
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_b(\mathbb{R}^d;\mathbb{R}^m)$ of bounded and continuous functions, associated to a class of nonautonomous weakly coupled…
We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…
This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…
We consider a discrete version of the Witsenhausen problem where all random variables are bounded and take on integer values. Our main goal is to understand the complexity of computing good strategies given the distributions for the initial…
We study pure exploration problems in which the set of correct answers is possibly infinite. For example, such problems arise when regressing a continuous function on the means of the bandit or when learning Nash equilibria by querying…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…
We consider the Cauchy problem of a dissipative nonlinear Schr\"odinger equation with a time dependent harmonic potential. We find a critical situation that the $L^2$-norm of dissipative solutions decays or not and which is decided by a…
The concern of this paper is the Cauchy problem for the Prandtl equation. This problem is known to be well-posed for analytic data, or for data with monotonicity properties. We prove here that it is linearly ill-posed in Sobolev type…
We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a…
This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem,…
In this note we discuss the conditional stability issue for the finite dimensional Calder\'on problem for the fractional Schr\"{o}dinger equation with a finite number of measurements. More precisely, we assume that the unknown potential $q…
The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case that the value function is assumed to be continuous…
A logarithmic type modulus of continuity is established for weak solutions to a two-phase Stefan problem, up to the parabolic boundary of a cylindrical space-time domain. For the Dirichlet problem, we merely assume that the spatial domain…
This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…
Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…