CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS变分法与偏微分方程
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS(英文缩写 CALC VAR PARTIAL DIF),ISSN 0944-2669,eISSN 1432-0835,中文译名:变分法与偏微分方程 是一本学术期刊。本页汇总该期刊的最新影响因子、分区信息以及最新收录于 PubMed 的文献,帮助您快速了解期刊全貌。
发文量统计区间：2025-09-27 至 2026-09-27，按本站收录文献的发表日期统计。
期刊介绍
历年影响因子趋势
| JCR 数据年份 | 影响因子 | JCR 分区 |
|---|---|---|
| 2021 | 2.079 | Q1 |
| 2022 | 2.100 | Q1 |
| 2023 | 2.100 | Q1 |
| 2024 | 2.000 | Q1 |
| 2025 | 2.100 | Q1 |
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 最新收录文献
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1. Average-field approximation for dilute almost-bosonic anyons.
PMID:日期:2026-01-01We study the ground state of a system of two-dimensional trapped almost-bosonic anyons. This setup can equivalently be viewed as bosons interacting through long-range magnetic potentials generated by magnetic charges carried by each particle. These magnetic charges are assumed to be smeared over discs of radius -a model known as . To recover the point-like anyons perspective, we consider the joint limit as . We rigorously justify the for any radius that decays polynomially, and even for certain exponentially decaying . The average-field approximation asserts that the particles behave like independent, identical bosons interacting through a self-consistent magnetic field. Our result significantly improves upon the best-known estimates from [1, 2], and it in particular covers radii that are much smaller than the mean interparticle distance. The proof strategy builds on a recent work on two-dimensional attractive Bose gases by Junge and the author [3].
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2. The global inverse fractional conductivity problem.
PMID:日期:2026-01-01We prove uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be nontrivial in the exterior of the domain and isotropic, while the data is given in the form of partial Dirichlet-to-Neumann (DN) maps measured in nondisjoint open subsets of the exterior. This can be seen as the fractional counterpart of the classical inverse conductivity problem. The proof is based on a unique continuation property (UCP) for the DN maps and a novel exterior determination method from the partial exterior DN maps, which is a nonlocal analog of the classical boundary determination method by Kohn and Vogelius. Exterior determination is achieved independently of the UCP and despite the nonlocality of the equation.
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3. How close is too close for singular mean curvature flows?
PMID:日期:2026-01-01Suppose , , are two mean curvature flows in encountering a multiplicity one compact singularity at time , in such a manner that for every , the Hausdorff distance between the two flows, , satisfies . We demonstrate that for every . This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where is itself a self-similarly shrinking flow.
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4. {"_":"Existence of nontrival -harmonic maps via min-max methods.","i":["n"]}
PMID:日期:2026-01-01For any and any closed manifold with for some , we establish the existence of nontrivial -harmonic maps from into . When , these maps naturally appear as bubbling limits of -harmonic maps with , obtained by min-max constructions in the limit .
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5. Free boundary minimal Möbius bands in toroids.
PMID:日期:2026-01-01We prove that round, strictly mean convex toroids of revolution contain infinitely many (geometrically distinct) embedded free boundary minimal Möbius bands as well as infinitely many embedded free boundary minimal annuli. The surfaces in both families are constructed by means of equivariant variational methods and their areas grow linearly with the order of their symmetry groups.
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6. On De Giorgi's conjecture of nonlocal approximations for free-discontinuity problems: The symmetric gradient case.
PMID:日期:2026-01-01We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class of continuous finite-difference approximants, we show the compactness of deformations with equibounded energies, as well as their Gamma-convergence. The compactness analysis is a crucial hurdle, which we overcome by generalizing a Fréchet-Kolmogorov approach previously introduced by two of the authors. A second essential difficulty is the identification of the limiting space of admissible deformations, since a control on the directional variations is, a priori, only available in average. A limiting representation in GSBD is eventually established via a novel characterization of this space.
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7. Thermo-elastodynamics of nonlinearly viscous solids.
PMID:日期:2026-01-01In this paper, we study the thermo-elastodynamics of nonlinearly viscous solids in the Kelvin-Voigt rheology where both the elastic and the viscous stress tensors comply with the frame-indifference principle. The system features a force balance including inertia in the frame of nonsimple materials and a heat-transfer equation which is governed by the Fourier law in the deformed configuration. Combining a staggered minimizing movement scheme for quasi-static thermoviscoelasticity [2, 37] with a variational approach to hyperbolic PDEs developed in [5], our main result consists in establishing the existence of weak solutions in the dynamic case. This is first achieved by including an additional higher-order regularization for the dissipation. Afterwards, this regularization can be removed by passing to a weaker formulation of the heat-transfer equation which complies with a total energy balance. The latter description hinges on regularity theory for the fourth order -Laplacian which induces regularity estimates of the deformation beyond the standard estimates available from energy bounds. Besides being crucial for the proof, these extra regularity properties might be of independent interest and seem to be new in the setting of nonlinear viscoelasticity, also in the static or quasi-static case.
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8. JKO schemes with general transport costs.
PMID:日期:2026-01-01We modify the JKO scheme, which is a time discretization of the Wasserstein gradient flow, by replacing the Wasserstein distance with more general transport costs on manifolds. We show when the cost function has a mixed Hessian which defines a Riemannian metric, our modified JKO scheme converges, under suitable conditions, to the corresponding Riemannian Fokker-Planck equation. Thus on a Riemannian manifold one may replace the (squared) Riemannian distance with any cost function which induces the metric. Of interest is when the Riemannian distance is computationally intractable, but a suitable cost has a simple analytic expression. We consider the Fokker-Planck equation on compact submanifolds with the Neumann boundary condition and on complete Riemannian manifolds with a finite drift condition. As an application we consider Hessian manifolds, taking as a cost the Bregman divergence.
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9. Parabolic-elliptic and indirect-direct simplifications in chemotaxis systems driven by indirect signalling.
PMID:日期:2026-01-01Singular limits for the following indirect signalling chemotaxis system are investigated. More precisely, we study parabolic-elliptic simplification, or PES, with fixed up to the critical dimension , and indirect-direct simplification, or IDS, up to the critical dimension . These are relevant in biological situations where the signalling process is on a much faster time scale compared to the species diffusion and all interactions. Showing singular limits in critical dimensions is challenging. To deal with the PES, we carefully combine the entropy function, an Adam-type inequality, the regularisation of slow evolution, and an energy equation method to obtain strong convergence in representative spaces. For the IDS, a bootstrap argument concerning the -energy function is devised, which allows us to obtain suitable uniform bounds for the singular limits. Moreover, in both scenarios, we also present the convergence rates, where the effect of the initial layer and the convergence to the critical manifold are also revealed.
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10. Explicit minimisers for anisotropic Riesz energies.
PMID:日期:2026-01-01In this paper we characterise the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. In particular we show that, if the Fourier transform of the repulsive potential is positive, the minimiser is supported on a fully-dimensional ellipsoid, and its density is given by a Barenblatt-type profile. Our technique of proof is based on a Fourier representation of the potential of such measures, that extends a previous formula established by some of the authors in the Coulomb case.