Related papers: The Aronsson equation, Lyapunov functions and loca…

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal…

We develop a "local theory" of multidimensional quasiperiodic $\SL(2,\R)$ cocycles which are not homotopic to a constant. It describes a $C^1$-open neighborhood of cocycles of rotations and applies irrespective of arithmetic conditions on…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…

We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…

We construct Hamiltonian Floer complexes associated to continuous, and even lower semi-continuous, time dependent exhaustion functions on geometrically bounded symplectic manifolds. We further construct functorial continuation maps…

In this paper, we address the existence of preferred asymptotic coordinates on asymptotically Euclidean (AE) manifolds $(M^3,g)$ such that $g$ admits an asymptotically Schwarzschildian first order expansion, based purely on a priori…

We investigate the properties of convex functions in the plane that satisfy a local inequality which generalizes the notion of sub-solution of Monge-Ampere equation for a Monge-Kantorovich problem with quadratic cost between non-absolutely…

A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…

We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge-Am\`ere equation on a general Hermitian manifold with non-empty boundary. We prove optimal subsolution theorems: for bounded and H\"older…

It was recently proven by De Lellis, Kappeler, and Topalov that the periodic Cauchy problem for the Camassa-Holm equations is locally well-posed in the space Lip (T) endowed with the topology of H^1 (T). We prove here that the Lagrangian…

We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely on each interval of monotonicity, but branching…

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…

We show that the spacing between eigenvalues of the discrete 1D Hamiltonian with arbitrary potentials which are bounded, and with Dirichlet or Neumann Boundary Conditions is bounded away from zero. We prove an explicit lower bound, given by…

Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…

In this article, we investigate the regularity for certain elliptic systems without a $L^2$-antisymmetric structure. As applications, we prove some $\epsilon$-regularity theorems for weakly harmonic maps from the unit ball $B= B(m) \subset…

We consider a second order non-autonomous system which can be interpreted as the Newtonian equation of motion on a Riemannian manifold under the action of time-quasiperiodic force field. The problem is to find conditions which ensures: (a)…

Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms…

We study the regularity of solutions to the fully nonlinear thin obstacle problem. We establish local $C^{1,\alpha}$ estimates on each side of the smooth obstacle, for some small $\alpha > 0$. Our results extend those of Milakis-Silvestre…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…