变分中一个非严格凸问题的唯一性结果

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-11-07 DOI:10.1051/cocv/2023079

Benjamin Lledos

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引用次数: 0

摘要

摘要证明了φ(∇v)−λv形式[[EQUATION]]变分学中非严格凸问题解的唯一性。这里φ是一个在原点不可微的凸函数，λ是一个Lipschitz函数。为了证明这一结果，我们证明了在相当一般的假设下，极小值是全局Lipschitz连续的。

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A uniqueness result for a non-strictly convex problem in the calculus of variations

Abstract. We prove the uniqueness of the solution for a non-strictly convex problem in the Calculus of Variations of the form [[EQUATION]] φ (∇ v ) − λv . Here, φ is a convex function not differentiable at the origin and λ is a Lipschitz function. To prove this result we show that under fairly general assumptions, the minimizers are globally Lipschitz continuous.

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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7.10%

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.