The Nonlinear Analysis section of the Annales de l'Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.

The Annales de l'Institut Henri Poincaré (C) Analyse Non Lineaire is an international journal established in 1983, focusing on the field of nonlinear analysis. It publishes original and high-quality research articles that cover all domains related to nonlinear analysis, particularly applicable to partial differential equations, mechanics, physics, and economics, while also addressing numerical aspects.

《Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire》是一本国际期刊，成立于1983年，专注于非线性分析领域，发表原创且高质量的研究文章。期刊涵盖与非线性分析相关的所有领域，特别是偏微分方程、力学、物理学和经济学等应用，同时也关注数值分析的相关内容。

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Matthias Kotschote

Annales de l Institut Henri Poincaré C Analyse Non Linéaire

Strong solutions for a compressible fluid model of Korteweg type

可压缩Korteweg型流体模型的强解

Filippo Gazzola

Marco Squassina

Global solutions and finite time blow up for damped semilinear wave equations

阻尼半线性波动方程的全局解与有限时间爆破

We study the non-linear BGK model in one dimension coupled to a spatially varying thermostat. We show existence, local uniqueness, and linear stability of a steady state when the linear coupling term is large compared to the non-linear self-interaction term. This model possesses a non-explicit spatially dependent non-equilibrium steady state. For the existence and the local uniqueness we utilise a fixed point argument, reducing the study of the non-linear model to the linear BGK model, while for the stability we adapt the L^{2} hypocoercivity theory, yielding existence of a spectral gap for the linearised operator around this non-equilibrium steady state.

Josephine Evans

Angeliki Menegaki

Properties of non-equilibrium steady states for the non-linear BGK equation on the torus

环面上非线性BGK方程非平衡稳态的性质

We study s -dependence for minimizing W^{s,n/s} -harmonic maps u\colon \mathbb{S}^{n} \to \mathbb{S}^{\ell} in homotopy classes. Sacks–Uhlenbeck theory shows that, for each s , minimizers exist in a generating subset of \pi_{n}(\mathbb{S}^{\ell}) . We show that this generating subset can be chosen locally constant in s . We also show that as s varies, the minimal W^{s,n/s} -energy in each homotopy class changes continuously. In particular, we provide progress on a question raised by Mironescu [in: Perspectives in nonlinear partial differential equations (2007), 413–436] and Brezis–Mironescu [Sobolev maps to the circle (2021)].

Katarzyna Mazowiecka

Armin Schikorra

$s$-stability for $W^{s,n/s}$-harmonic maps in homotopy groups

$s$-稳定性对于同伦群中的$W^{s,n/s}$-调和映射

We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton–Jacobi–Bellman equation, which is set on the set of probability measures. We introduce a new definition of viscosity solutions of this equation, which yields general comparison principles, in particular for cases involving terms modeling stochasticity in the optimal control problem. We are then able to establish results of existence and uniqueness of viscosity solutions of the Hamilton–Jacobi–Bellman equation. These results rely on controllability results for stochastic optimal transport that we also establish.

Charles Bertucci

Stochastic optimal transport and Hamilton–Jacobi–Bellman equations on the set of probability measures

概率测度集上的随机最优传输与Hamilton-Jacobi-Bellman方程

In this paper we extend the scope of Caffarelli’s contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in \mathbb{R}^{d} . Our focus is on a broader category of densities, specifically those that are \frac{1}{d} -concave and can be represented as V^{-d} , where V is convex. By setting appropriate conditions, we derive linear or sublinear limitations for the optimal transport map. This leads us to a comprehensive Lipschitz estimate that aligns with the principles established in Caffarelli’s theorem.

Guillaume Carlier

Alessio Figalli

Filippo Santambrogio

On optimal transport maps between $\frac{1}{d}$-concave densities

关于 $\frac{1}{d}$-凹密度之间的最优传输映射

In this work we examine the stability of some classes of integrals, in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing at infinity, which has recently been examined in the framework of elliptic PDEs. We use localization techniques and higher-integrability Meyers-type results to provide a closure theorem by \Gamma -convergence within a large class of integral functionals. From such a result we derive stability theorems in homogenization which comprise the case of perturbations with zero average on the whole space. The results are also extended to the stochastic case, and specialized to the G -convergence of operators corresponding to quadratic forms. A corresponding analysis is also carried out for non-symmetric operators using the localization properties of H -convergence. Finally, we treat the case of perforated domains with Neumann boundary condition, and their stability.

Abbreviation	Ann. Inst. H. Poincaré Anal. Non Linéaire
Journal Impact	1.92
Quartiles(Global)	MATHEMATICS, APPLIED(Q1)

ISSN	0294-1449, 1873-1430
h-index	76

Publication Information	Publisher: European Mathematical Society Publishing House，Publishing cycle: Bimonthly，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 1984，Proportion of original research papers: 100.00%，Self Citation Rate:5.60%， Gold OA Rate: 62.12%
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：较易

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

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Strong solutions for a compressible fluid model of Korteweg type

Global solutions and finite time blow up for damped semilinear wave equations

Properties of non-equilibrium steady states for the non-linear BGK equation on the torus

$s$-stability for $W^{s,n/s}$-harmonic maps in homotopy groups

Stochastic optimal transport and Hamilton–Jacobi–Bellman equations on the set of probability measures

Properties of non-equilibrium steady states for the non-linear BGK equation on the torus

$s$-stability for $W^{s,n/s}$-harmonic maps in homotopy groups

Stochastic optimal transport and Hamilton–Jacobi–Bellman equations on the set of probability measures

On optimal transport maps between $\frac{1}{d}$-concave densities

A closure theorem for $\Gamma$-convergence and $H$-convergence with applications to non-periodic homogenization