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Extremal mappings of finite distortion and the Radon–Riesz property 有限畸变的极值映射和Radon-Riesz性质
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-05-03 DOI: 10.4171/rmi/1379
G. Martin, Cong Yao
{"title":"Extremal mappings of finite distortion and the Radon–Riesz property","authors":"G. Martin, Cong Yao","doi":"10.4171/rmi/1379","DOIUrl":"https://doi.org/10.4171/rmi/1379","url":null,"abstract":"We consider Sobolev mappings f ∈ W (Ω,C), 1 < q < ∞, between planar domains Ω ⊂ C. We analyse the Radon-Riesz property for convex functionals of the form f 7→ ∫ Ω Φ(|Df(z)|, J(z, f)) dz and show that under certain criteria, which hold in important cases, weak convergence in W 1,q loc (Ω) of (for instance) a minimising sequence can be improved to strong convergence. This finds important applications in the minimisation problems for mappings of finite distortion and the L and Exp -Teichmüller theories.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42317708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Local well-posedness for the gKdV equation on the background of a bounded function 有界函数背景下gKdV方程的局部适定性
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-04-30 DOI: 10.4171/rmi/1345
J. M. Palacios
{"title":"Local well-posedness for the gKdV equation on the background of a bounded function","authors":"J. M. Palacios","doi":"10.4171/rmi/1345","DOIUrl":"https://doi.org/10.4171/rmi/1345","url":null,"abstract":"We prove the local well-posedness for the generalized Korteweg-de Vries equation in H(R), s > 1/2, under general assumptions on the nonlinearity f(x), on the background of an Lt,x-function Ψ(t, x), with Ψ(t, x) satisfying some suitable conditions. As a consequence of our estimates, we also obtain the unconditional uniqueness of the solution in H(R). This result not only gives us a framework to solve the gKdV equation around a Kink, for example, but also around a periodic solution, that is, to consider localized non-periodic perturbations of a periodic solution. As a direct corollary, we obtain the unconditional uniqueness of the gKdV equation in H(R) for s > 1/2. We also prove global existence in the energy space H(R), in the case where the nonlinearity satisfies that |f (x)| . 1.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45585769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Gibbs measures as unique KMS equilibrium states of nonlinear Hamiltonian PDEs Gibbs测度是非线性哈密顿偏微分方程的唯一KMS平衡态
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-02-24 DOI: 10.4171/rmi/1366
Z. Ammari, Vedran Sohinger
{"title":"Gibbs measures as unique KMS equilibrium states of nonlinear Hamiltonian PDEs","authors":"Z. Ammari, Vedran Sohinger","doi":"10.4171/rmi/1366","DOIUrl":"https://doi.org/10.4171/rmi/1366","url":null,"abstract":"The classical Kubo-Martin-Schwinger (KMS) condition is a fundamental property of statistical mechanics characterizing the equilibrium of infinite classical mechanical systems. It was introduced in the seventies by G. Gallavotti and E. Verboven as an alternative to the Dobrushin-Lanford-Ruelle (DLR) equation. In this article, we consider this concept in the framework of nonlinear Hamiltonian PDEs and discuss its relevance. In particular, we prove that Gibbs measures are the unique KMS equilibrium states for such systems. Our proof is based on Malliavin calculus and Gross-Sobolev spaces. The main feature of our work is the applicability of our results to the general context of white noise, abstract Wiener spaces and Gaussian probability spaces, as well as to fundamental examples of PDEs like the nonlinear Schrodinger, Hartree, and wave (Klein-Gordon) equations.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48686528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 4
General $delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation 二维Dirac算子的一般$delta$壳层相互作用：自邻接性和近似
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-02-19 DOI: 10.4171/RMI/1354
B. Cassano, V. Lotoreichik, A. Mas, Matvej Tuvsek
{"title":"General $delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation","authors":"B. Cassano, V. Lotoreichik, A. Mas, Matvej Tuvsek","doi":"10.4171/RMI/1354","DOIUrl":"https://doi.org/10.4171/RMI/1354","url":null,"abstract":"In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator, and moreover we describe its approximation by Dirac operators with regular potentials.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48284434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 17
Poincaré series of multiplier and test ideals 庞加莱系列乘数和试验理想
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-02-16 DOI: 10.4171/rmi/1347
J. À. Montaner, Luis N'unez-Betancourt
{"title":"Poincaré series of multiplier and test ideals","authors":"J. À. Montaner, Luis N'unez-Betancourt","doi":"10.4171/rmi/1347","DOIUrl":"https://doi.org/10.4171/rmi/1347","url":null,"abstract":"We prove the rationality of the Poincar'e series of multiplier ideals in any dimension and thus extending the main results for surfaces of Galindo and Monserrat and Alberich-Carrami~nana et al. Our results also hold for Poincar'e series of test ideals. In order to do so, we introduce a theory of Hilbert functions indexed over $mathbb{R}$ which gives an unified treatment of both cases.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44063679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On the core of a low dimensional set-valued mapping 关于低维集值映射的核
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-02-15 DOI: 10.4171/rmi/1334
P. Shvartsman
{"title":"On the core of a low dimensional set-valued mapping","authors":"P. Shvartsman","doi":"10.4171/rmi/1334","DOIUrl":"https://doi.org/10.4171/rmi/1334","url":null,"abstract":"LetM = (M, ρ) be a metric space and let X be a Banach space. Let F be a setvalued mapping fromM into the family Km(X) of all compact convex subsets of X of dimension at most m. The main result in our recent joint paper [16] with Charles Fefferman (which is referred to as a “Finiteness Principle for Lipschitz selections”) provides efficient conditions for the existence of a Lipschitz selection of F, i.e., a Lipschitz mapping f :M→ X such that f (x) ∈ F(x) for every x ∈ M. We give new alternative proofs of this result in two special cases. When m = 2 we prove it for X = R, and when m = 1 we prove it for all choices of X. Both of these proofs make use of a simple reiteration formula for the “core” of a set-valued mapping F, i.e., for a mapping G :M→ Km(X) which is Lipschitz with respect to the Hausdorff distance, and such that G(x) ⊂ F(x) for all x ∈ M.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48692843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Falconer’s $(K, d)$ distance set conjecture can fail for strictly convex sets $K$ in $mathbb R^d$ Falconer的$(K, d)$距离集猜想对于$mathbb R^d$中的严格凸集$K$是不成立的
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-02-08 DOI: 10.4171/RMI/1254
C. Bishop, H. Drillick, Dimitrios Ntalampekos
{"title":"Falconer’s $(K, d)$ distance set conjecture can fail for strictly convex sets $K$ in $mathbb R^d$","authors":"C. Bishop, H. Drillick, Dimitrios Ntalampekos","doi":"10.4171/RMI/1254","DOIUrl":"https://doi.org/10.4171/RMI/1254","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":"19 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89585916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operators Bergman空间上Toeplitz算子的迹估计及其在复合算子上的应用
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-01-28 DOI: 10.4171/rmi/1303
O. El-Fallah, M. E. Ibbaoui
{"title":"Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operators","authors":"O. El-Fallah, M. E. Ibbaoui","doi":"10.4171/rmi/1303","DOIUrl":"https://doi.org/10.4171/rmi/1303","url":null,"abstract":"Let $Omega$ be a subdomain of $mathbb{C}$ and let $mu$ be a positive Borel measure on $Omega$. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator $T_mu$ acting on Bergman spaces on $Omega$. Let $(lambda_n(T_mu))$ be the decreasing sequence of the eigenvalues of $T_mu$ and let $rho$ be an increasing function such that $rho (n)/n^A$ is decreasing for some $A>0$. We give an explicit necessary and sufficient geometric condition on $mu$ in order to have $lambda_n(T_mu)asymp 1/rho (n)$. As applications, we consider composition operators $C_varphi$, acting on some standard analytic spaces on the unit disc $mathbb{D}$. First, we give a general criterion ensuring that the singular values of $C_varphi$ satisfy $s_n(C_varphi ) asymp 1/rho(n)$. Next, we focus our attention on composition operators with univalent symbols, where we express our general criterion in terms of the harmonic measure of $varphi mathbb{D})$. We finally study the case where $partial varphi (mathbb{D})$ meets the unit circle in one point and give several concrete examples. Our method is based on upper and lower estimates of the trace of $h(T_mu)$, where $h$ is suitable concave or convex functions.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48898837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
Smooth linearization under nonuniform hyperbolicity 非均匀双曲下的光滑线性化
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-01-12 DOI: 10.4171/RMI/1249
L. Barreira, C. Valls
{"title":"Smooth linearization under nonuniform hyperbolicity","authors":"L. Barreira, C. Valls","doi":"10.4171/RMI/1249","DOIUrl":"https://doi.org/10.4171/RMI/1249","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77855319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Interpolation of power mappings 幂映射的插值
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-01-11 DOI: 10.4171/rmi/1359
Jack Burkart, K. Lazebnik
{"title":"Interpolation of power mappings","authors":"Jack Burkart, K. Lazebnik","doi":"10.4171/rmi/1359","DOIUrl":"https://doi.org/10.4171/rmi/1359","url":null,"abstract":". Let ( M j ) ∞ j =1 ∈ N and ( r j ) ∞ j =1 ∈ R + be increasing sequences satisfying some mild rate of growth conditions. We prove that there is an entire function f : C → C whose behavior in the large annuli { z ∈ C : r j · exp( π/M j ) ≤ | z | ≤ r j +1 } is given by a perturbed rescaling of z (cid:55)→ z M j , such that the only singular values of f are rescalings of ± r M j j . We describe several applications to the dynamics of entire functions.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42960580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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