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A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS 一维NLS的Sobolev概周期不变环面构造注记
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-15 DOI: 10.4171/rlm/923
Luca Biasco, Jessica Elisa Massetti, Michela Procesi
{"title":"A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS","authors":"Luca Biasco, Jessica Elisa Massetti, Michela Procesi","doi":"10.4171/rlm/923","DOIUrl":"https://doi.org/10.4171/rlm/923","url":null,"abstract":"We announce a method for the construction of almost periodic solutions of the one dimensional analytic NLS with only Sobolev regularity both in time and space. This is the first result of this kind for PDEs.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"46 7","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138523886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Higher differentiability for a class of obstacle problems with nearly linear growth conditions 一类具有近线性增长条件的障碍物问题的高可微性
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-15 DOI: 10.4171/RLM/914
Chiara Gavioli
{"title":"Higher differentiability for a class of obstacle problems with nearly linear growth conditions","authors":"Chiara Gavioli","doi":"10.4171/RLM/914","DOIUrl":"https://doi.org/10.4171/RLM/914","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"28 1","pages":"767-789"},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72770046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces 变指数向量值勒贝格空间上的大数加权强律
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-15 DOI: 10.4171/RLM/915
F. Mukhamedov, H. Rafeiro
{"title":"Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces","authors":"F. Mukhamedov, H. Rafeiro","doi":"10.4171/RLM/915","DOIUrl":"https://doi.org/10.4171/RLM/915","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"15 1","pages":"791-814"},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78783816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hilbert-type inequalities in homogeneous cones 齐次锥中的hilbert型不等式
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-15 DOI: 10.4171/RLM/916
G. Garrigós, C. Nana
{"title":"Hilbert-type inequalities in homogeneous cones","authors":"G. Garrigós, C. Nana","doi":"10.4171/RLM/916","DOIUrl":"https://doi.org/10.4171/RLM/916","url":null,"abstract":"We prove L-L bounds for the class of Hilbert-type operators associated with generalized powers Q in a homogeneous cone Ω. Our results extend and slightly improve earlier work from [10], where the problem was considered for scalar powers α = (α, . . . , α) and symmetric cones Ω. We give a more transparent proof, provide new examples, and briefly discuss a long standing open question regarding characterization of L boundedness for the case of vector indices α.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"33 6","pages":"815-838"},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72474598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Positive solution to Schrödinger equation with singular potential and double critical exponents 具有奇异势和双临界指数的Schrödinger方程的正解
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-15 DOI: 10.4171/RLM/910
Yujian Su
{"title":"Positive solution to Schrödinger equation with singular potential and double critical exponents","authors":"Yujian Su","doi":"10.4171/RLM/910","DOIUrl":"https://doi.org/10.4171/RLM/910","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"14 1","pages":"667-698"},"PeriodicalIF":0.5,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73961734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Smooth homeomorphic approximation of piecewise affine homeomorphisms 分段仿射同胚的光滑同胚逼近
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-02-12 DOI: 10.4171/rlm/946
D. Campbell, Filip Soudsk'y
{"title":"Smooth homeomorphic approximation of piecewise affine homeomorphisms","authors":"D. Campbell, Filip Soudsk'y","doi":"10.4171/rlm/946","DOIUrl":"https://doi.org/10.4171/rlm/946","url":null,"abstract":"Given any f a locally finitely piecewise affine homeomorphism of Ω ⊂ R n onto ∆ ⊂ R in W , 1 ≤ p < ∞ and any ε > 0 we construct a smooth injective map f̃ such that ‖f − f̃‖W (Ω,R) < ε.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48890958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Multipoint Julia theorems 多点Julia定理
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-01-10 DOI: 10.4171/rlm/950
M. Abate
{"title":"Multipoint Julia theorems","authors":"M. Abate","doi":"10.4171/rlm/950","DOIUrl":"https://doi.org/10.4171/rlm/950","url":null,"abstract":"Following ideas introduced by Beardon-Minda and by BaribeauRivard-Wegert in the context of the Schwarz-Pick lemma, we use the iterated hyperbolic difference quotients to prove a multipoint Julia lemma. As applications, we give a sharp estimate from below of the angular derivative at a boundary point, generalizing results due to Osserman, Mercer and others; and we prove a generalization to multiple fixed points of an interesting estimate due to Cowen and Pommerenke. These applications show that iterated hyperbolic difference quotients and multipoint Julia lemmas can be useful tools for exploring in a systematic way the influence of higher order derivatives on the boundary behaviour of holomorphic self-maps of the unit disk.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46495645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Punctual characterization of the unitary flat bundle of weight one PVHS and application to families of curves 重一PVHS的酉平丛的穿刺特征及其在曲线族中的应用
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-01-08 DOI: 10.4171/rlm/987
Víctor González-Alonso, Sara Torelli
{"title":"Punctual characterization of the unitary flat bundle of weight one PVHS and application to families of curves","authors":"Víctor González-Alonso, Sara Torelli","doi":"10.4171/rlm/987","DOIUrl":"https://doi.org/10.4171/rlm/987","url":null,"abstract":"In this paper we consider the problem of pointwise determining the fibres of the flat unitary subbundle of a PVHS of weight one. Starting from the associated Higgs field, and assuming the base has dimension $1$, we construct a family of (smooth but possibly non-holomorphic) morphisms of vector bundles with the property that the intersection of their kernels at a general point is the fibre of the flat subbundle. We explore the first one of these morphisms in the case of a geometric PVHS arising from a family of smooth projective curves, showing that it acts as the cup-product with some sort of\"second-order Kodaira-Spencer class\"which we introduce, and check in the case of a family of smooth plane curves that this additional condition is non-trivial.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47581288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
On topologically trivial automorphisms of compact Kähler manifolds and algebraic surfaces 紧致Kähler流形和代数曲面的拓扑平凡自同构
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-12-21 DOI: 10.4171/RLM/933
F. Catanese, Wenfei Liu
{"title":"On topologically trivial automorphisms of compact Kähler manifolds and algebraic surfaces","authors":"F. Catanese, Wenfei Liu","doi":"10.4171/RLM/933","DOIUrl":"https://doi.org/10.4171/RLM/933","url":null,"abstract":"In this paper, we investigate automorphisms of compact Kähler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of C∞-isotopically trivial automorphisms, resp. cohomologically trivial automorphisms, have a number of connected components which can be arbitrarily large. Dedicated to the memory of the ‘red’ Bishop of Italian Mathematics, Edoardo Vesentini (1928-2020).","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48924001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Interacting particle systems with long-range interactions: scaling limits and kinetic equations 具有长程相互作用的相互作用粒子系统：标度极限和动力学方程
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-12-09 DOI: 10.4171/RLM/939
A. Nota, J. Velázquez, Raphael Winter
{"title":"Interacting particle systems with long-range interactions: scaling limits and kinetic equations","authors":"A. Nota, J. Velázquez, Raphael Winter","doi":"10.4171/RLM/939","DOIUrl":"https://doi.org/10.4171/RLM/939","url":null,"abstract":"The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a friction term which is due to the interaction with the surrounding particles. Some of the technical details of this method are discussed in the companion paper [47].","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44492638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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