21 citations · 60 across the 7 of their papers we have counts for
7 papers
Large-time asymptotics in deep learning
Carlos Esteve, Borjan Geshkovski, Dario Pighin +1
We consider the neural ODE perspective of supervised learning and study the impact of the final time (which may indicate the depth of a corresponding ResNet) in training. For t…
The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems
Carlos Esteve, Hicham Kouhkouh, Dario Pighin +1
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal…
The inverse problem for Hamilton-Jacobi equations and semiconcave envelopes
Carlos Esteve, Enrique Zuazua
We study the inverse problem, or inverse design problem, for a time-evolution Hamilton-Jacobi equation. More precisely, given a target function and a time horizon , we a…
Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature
Carlos Esteve
We consider the diffusive Hamilton-Jacobi equation in a bounded planar domain with zero Dirichlet boundary condition. It is known that, for , the sol…
The evolution problem associated with eigenvalues of the Hessian
Pablo Blanc, Carlos Esteve, Julio D. Rossi
In this paper we study the evolution problem \[ \left\lbrace\begin{array}{ll} u_t (x,t)- λ_j(D^2 u(x,t)) = 0, & \text{in } Ω\times (0,+\infty), \\ u(x,t) = g(x,t), & \text{on } \pa…
Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity
Carlos Esteve, Philippe Souplet
We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, based on a parabolic equation with singular nonlinearity. We study…
No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem
Carlos Esteve, Philippe Souplet
We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, involving a parabolic equation with singular nonlinearity. We study…