Carlos Esteve – cmc.deusto.eus

Large-time asymptotics in deep learning

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

C. Esteve, B. Geshkovski, D. Pighin, E. Zuazua (2025) Large-time asymptotics in deep learning, https://hal.archives-ouvertes.fr/hal-02912516 Abstract. We consider the neural ODE perspective of supervised learning and study the impact of the…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

C. Esteve, E. Zuazua. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws Nonlinear Analysis, Vol. 227, https://doi.org/10.1016/j.na.2022.113167 Abstract. We give a full characterization of the range…

Multilevel Selective Harmonic Modulation via Optimal Control

U. Biccari, C. Esteve-Yagüe, D.J. Oroya-Villalta (2022) Multilevel Selective Harmonic Modulation via Optimal Control., Appl Math Optim, Vol. 86, No. 43, https://doi.org/10.1007/s00245-022-09917-5 Abstract. We consider the Selective Harmonic Modulation (SHM) problem,…

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

C. Esteve, E. Zuazua. Differentiability with respect to the initial condition for Hamilton-Jacobi equations (2022) SIAM Journal on Mathematical Analysis, Vol. 54, No. 5, pp. 5388-5423 https://doi.org/10.1137/22M1469353 Abstract. We prove…

The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems. Math. Control Signals Syst. (2022). https://doi.org/10.1007/s00498-022-00325-2 Abstract:…

Turnpike in Lipschitz-nonlinear optimal control

Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control Nonlinearity. Vol 5. No. 34, pp. 1652-1701 (2022) https://doi.org/10.1088/1361-6544/ac4e61 Abstract. We present a new proof of…

Sparse approximation in learning via neural ODEs

deep learning, Neural ODEs, Nonlinear systems, optimal control, Sparsity, Supervised Learning

Esteve C., Geshkovski B. Sparse approximation in learning via neural ODEs (2021) Abstract. We consider the continuous-time, neural ordinary differential equation (neural ODE) perspective of deep supervised learning, and study the…

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Hamilton-Jacobi equation, inverse design problem, obstacle problems, semiconcave envelopes

Esteve C., Zuazua E.. The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes SIAM J. Math. Anal., Vol. 52, No. 6, pp. 5627–5657 (2020). https://doi.org/10.1137/20M1330130 Abstract. We study the inverse…

Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem

decay rates, nonlocal diffusion

C. Esteve, J.D. Rossi, A. San Antolín. Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem. BOUND VALUE PROBL (2014), pp. 109. DOI: 10.1186/1687-2770-2014-109 Abstract. We obtain…

Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity

C. Esteve, Ph Souplet. Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity, NONLINEARITY, Vol. 31, No. 11 (2018). DOI: 10.1088/1361-6544 Abstract. We consider a well-known model for…

The evolution problem associated with eigenvalues of the Hessian

P. Blanc, C. Esteve, J. D. Rossi. The evolution problem associated with eigenvalues of the Hessian. J. London Math. Soc. (2020). https://doi.org/10.1112/jlms.12363 Abstract. In this paper we study the evolution…

Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature

C. Esteve Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvatureJ MATH PURE APPL, Vol 137 (2020) pp. 143-177, DOI: 10.1016/j.matpur.2019.12.006 Abstract. We consider…

No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem

C. Esteve, Ph. Souplet, No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem Adv. Differential Equ. Vol. 24, No. 7/8 (2019), pp. 465-500 https://projecteuclid.org/euclid.ade/1556762456…