Analysis & PDE最新文献_第8页

Overdetermined boundary problems with nonconstant Dirichlet and Neumann data 非常Dirichlet和Neumann数据的过定边界问题

IF 2.2 1区数学

Analysis & PDE Pub Date : 2023-11-11 DOI: 10.2140/apde.2023.16.1989

Miguel Domínguez-Vázquez, Alberto Enciso, Daniel Peralta-Salas

引用次数: 2

A characterization of the Razak–Jacelon algebra Razak-Jacelon代数的一个表征

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1799

Norio Nawata

{"title":"A characterization of the Razak–Jacelon algebra","authors":"Norio Nawata","doi":"10.2140/apde.2023.16.1799","DOIUrl":"https://doi.org/10.2140/apde.2023.16.1799","url":null,"abstract":"Combing Elliott, Gong, Lin and Niu's result and Castillejos and Evington's result, we see that if $A$ is a simple separable nuclear monotracial C$^*$-algebra, then $Aotimesmathcal{W}$ is isomorphic to $mathcal{W}$ where $mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we give another proof of this. In particular, we show that if $mathcal{D}$ is a simple separable nuclear monotracial $M_{2^{infty}}$-stable C$^*$-algebra which is $KK$-equivalent to ${0}$, then $mathcal{D}$ is isomorphic to $mathcal{W}$ without considering tracial approximations of C$^*$-algebras with finite nuclear dimension. Our proof is based on Matui and Sato's technique, Schafhauser's idea in his proof of the Tikuisis-White-Winter theorem and properties of Kirchberg's central sequence C$^*$-algebra $F(mathcal{D})$ of $mathcal{D}$. Note that some results for $F(mathcal{D})$ is based on Elliott-Gong-Lin-Niu's stable uniqueness theorem. Also, we characterize $mathcal{W}$ by using properties of $F(mathcal{W})$. Indeed, we show that a simple separable nuclear monotracial C$^*$-algebra $D$ is isomorphic to $mathcal{W}$ if and only if $D$ satisfies the following properties:(i) for any $thetain [0,1]$, there exists a projection $p$ in $F(D)$ such that $tau_{D, omega}(p)=theta$,(ii) if $p$ and $q$ are projections in $F(D)$ such that $0<tau_{D, omega}(p)=tau_{D, omega}(q)$, then $p$ is Murray-von Neumann equivalent to $q$,(iii) there exists a homomorphism from $D$ to $mathcal{W}$.","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136182101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

A general notion of uniform ellipticity and the regularity of the stress field for elliptic equations in divergence form 均匀椭圆性的一般概念和散度椭圆方程应力场的规律性

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1955

Umberto Guarnotta, Sunra Mosconi

引用次数: 9

Bosons in a double well: two-mode approximation and fluctuations 双阱中的玻色子:双模近似和涨落

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1885

Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner

引用次数: 2

Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds 共形横向各向异性流形上非线性磁性Schrödinger方程的反问题

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1825

Katya Krupchyk, Gunther Uhlmann

引用次数: 17

Discrete velocity Boltzmann equations in the plane: stationary solutions 平面上的离散速度玻尔兹曼方程:平稳解

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1869

Leif Arkeryd, Anne Nouri

引用次数: 0

Ground state properties in the quasiclassical regime 准经典状态下的基态性质

1区数学

Analysis & PDE Pub Date : 2023-10-16 DOI: 10.2140/apde.2023.16.1745

Michele Correggi, Marco Falconi, Marco Olivieri

引用次数: 9

A structure theorem for elliptic and parabolic operators with applications to homogenization of operators of Kolmogorov type 椭圆型和抛物型算子的结构定理及其在Kolmogorov型算子均匀化中的应用

1区数学

Analysis & PDE Pub Date : 2023-09-21 DOI: 10.2140/apde.2023.16.1547

Malte Litsgård, Kaj Nyström

{"title":"A structure theorem for elliptic and parabolic operators with applications to homogenization of operators of Kolmogorov type","authors":"Malte Litsgård, Kaj Nyström","doi":"10.2140/apde.2023.16.1547","DOIUrl":"https://doi.org/10.2140/apde.2023.16.1547","url":null,"abstract":"We consider the operators [ nabla_Xcdot(A(X)nabla_X), nabla_Xcdot(A(X)nabla_X)-partial_t, nabla_Xcdot(A(X)nabla_X)+Xcdotnabla_Y-partial_t, ] where $Xin Omega$, $(X,t)in Omegatimes mathbb R$ and $(X,Y,t)in Omegatimes mathbb R^mtimes mathbb R$, respectively, and where $Omegasubsetmathbb R^m$ is a (unbounded) Lipschitz domain with defining function $psi:mathbb R^{m-1}tomathbb R$ being Lipschitz with constant bounded by $M$. Assume that the elliptic measure associated to the first of these operators is mutually absolutely continuous with respect to the surface measure $mathrm{d} sigma(X)$, and that the corresponding Radon-Nikodym derivative or Poisson kernel satisfies a scale invariant reverse H\"older inequalities in $L^p$, for some fixed $p$, $1<p<infty$, with constants depending only on the constants of $A$, $m$ and the Lipschitz constant of $psi$, $M$. Under this assumption we prove that then the same conclusions are also true for the parabolic measures associated to the second and third operator with $mathrm{d} sigma(X)$ replaced by the surface measures $mathrm{d} sigma(X)mathrm{d} t$ and $mathrm{d} sigma(X)mathrm{d} Ymathrm{d} t$, respectively. This structural theorem allows us to reprove several results previously established in the literature as well as to deduce new results in, for example, the context of homogenization for operators of Kolmogorov type. Our proof of the structural theorem is based on recent results established by the authors concerning boundary Harnack inequalities for operators of Kolmogorov type in divergence form with bounded, measurable and uniformly elliptic coefficients.","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Simplices in thin subsets of Euclidean spaces 欧几里得空间的稀疏子集中的单形

1区数学

Analysis & PDE Pub Date : 2023-09-21 DOI: 10.2140/apde.2023.16.1485

Alex Iosevich, Akos Magyar

引用次数: 9

Resonances for Schrödinger operators on infinite cylinders and other products 无限圆柱体和其他产品上Schrödinger算子的共振

1区数学

Analysis & PDE Pub Date : 2023-09-21 DOI: 10.2140/apde.2023.16.1497

Christiansen, T. J.

{"title":"Resonances for Schrödinger operators on infinite cylinders and other products","authors":"Christiansen, T. J.","doi":"10.2140/apde.2023.16.1497","DOIUrl":"https://doi.org/10.2140/apde.2023.16.1497","url":null,"abstract":"We study the resonances of Schr\"odinger operators on the infinite product $X=mathbb{R}^dtimes mathbb{S}^1$, where $d$ is odd, $mathbb{S}^1$ is the unit circle, and the potential $Vin L^infty_c(X)$. This paper shows that at high energy, resonances of the Schr\"odinger operator $-Delta +V$ on $X=mathbb{R}^dtimes mathbb{S}^1$ which are near the continuous spectrum are approximated by the resonances of $-Delta +V_0$ on $X$, where the potential $V_0$ given by averaging $V$ over the unit circle. These resonances are, in turn, given in terms of the resonances of a Schr\"odinger operator on $mathbb{R}^d$ which lie in a bounded set. If the potential is smooth, we obtain improved localization of the resonances, particularly in the case of simple, rank one poles of the corresponding scattering resolvent on $mathbb{R}^d$. In that case, we obtain the leading order correction for the location of the corresponding high energy resonances. In addition to direct results about the location of resonances, we show that at high energies away from the resonances, the resolvent of the model operator $-Delta+V_0$ on $X$ approximates that of $-Delta+V$ on $X$. If $d=1$, in certain cases this implies the existence of an asymptotic expansion of solutions of the wave equation. Again for the special case of $d=1$, we obtain a resonant rigidity type result for the zero potential among all real-valued potentials.","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2