Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities [0.03%]
非局部波方程的最优Runge逼近及多项式非线性的唯一决定性
Yi-Hsuan Lin,Teemu Tyni,Philipp Zimmermann
Yi-Hsuan Lin
The main purpose of this article is to establish the Runge-type approximation in L 2 ( 0 , T ; H ~ s ( Ω ) ) for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical...
Georg C Hofstätter,Jonas Knoerr
Georg C Hofstätter
We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant with respect to volume-preserving linear maps. We thereby i...
Stability analysis of the incompressible porous media equation and the Stokes transport system via energy structure [0.03%]
能量结构下的不可压缩多孔介质方程与Stokes传输系统的稳定性分析
Jaemin Park
Jaemin Park
In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the v...
[Formula: see text] -Limsup estimate for a nonlocal approximation of the Willmore functional [0.03%]
非局部Willmore泛函逼近的[Formula: see text]-上极限估计公式
Hardy Chan,Mattia Freguglia,Marco Inversi
Hardy Chan
We propose a possible nonlocal approximation of the Willmore functional, in the sense of Gamma-convergence, based on the first variation of the fractional Allen-Cahn energies, and we prove the corresponding Γ -limsup estimate. Our anal...
Continuity up to the boundary for minimizers of the one-phase Bernoulli problem [0.03%]
一类单相Bernoulli问题极小元的边界正则性
Xavier Fernández-Real,Florian Gruen
Xavier Fernández-Real
We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and Hölder-continuous boundary data. As an application, we use the...
The nonlinear fast diffusion equation on smooth metric measure spaces: Hamilton-Souplet-Zhang estimates and a Ricci-Perelman super flow [0.03%]
光滑测度空间上非线性快速扩散方程：Hamilton-Souplet-Zhang估计及Ricci-Perelman超流体方程解的性质研究
Ali Taheri,Vahideh Vahidifar
Ali Taheri
This article presents new gradient estimates for positive solutions to the nonlinear fast diffusion equation on smooth metric measure spaces, involving the f-Laplacian. The gradient estimates of interest are of Hamilton-Souplet-Zhang or ell...
Globally stable blowup profile for supercritical wave maps in all dimensions [0.03%]
超临界波映射在所有维度上全局稳定的爆破剖面
Irfan Glogić
Irfan Glogić
We consider wave maps from the ( 1 + d ) -dimensional Minkowski space into the d-sphere. It is known from the work of Bizoń and Biernat (Commun Math Phys 338(3): 1443-1450, 2015) that in the energy-supercritical case, i.e., for d ≥ ...
A Esposito,R S Gvalani,A Schlichting et al.
A Esposito et al.
The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous i...
Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions [0.03%]
高维调和映射热流收缩解的存在性和稳定性
Irfan Glogić,Sarah Kistner,Birgit Schörkhuber
Irfan Glogić
We study singularity formation for the heat flow of harmonic maps from R d . For each d ≥ 4 , we construct a compact, d-dimensional, rotationally symmetric target manifold that allows for the existence of a corotational self-simila...
Traveling waves and effective mass for the regularized Landau-Pekar equations [0.03%]
正则化朗道-佩卡方程的行波和有效质量
Simone Rademacher
Simone Rademacher
We consider the regularized Landau-Pekar equations with positive speed of sound and prove the existence of subsonic traveling waves. We provide a definition of the effective mass for the regularized Landau-Pekar equations based on the energ...