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Some useful tools in the study of nonlinear elliptic problems 研究非线性椭圆问题的一些有用工具
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-09-16 DOI: 10.1016/j.exmath.2024.125616
Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu
{"title":"Some useful tools in the study of nonlinear elliptic problems","authors":"Nikolaos S. Papageorgiou ,&nbsp;Vicenţiu D. Rădulescu","doi":"10.1016/j.exmath.2024.125616","DOIUrl":"10.1016/j.exmath.2024.125616","url":null,"abstract":"<div><p>This paper gives an overview of some basic aspects concerning the qualitative analysis of nonlinear, nonhomogeneous elliptic problems. We are concerned with two classes of elliptic equations with Dirichlet boundary condition. The first problem is driven by a general nonhomogeneous differential operator, which includes several usual operators (such as the <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplace operator introduced by P. Marcellini). Next, we focus on differential operators with unbalanced growth in the nonautonomous case. Our analysis will point out some relevant differences between balanced and unbalanced growth problems. The presentation is done in the context of Dirichlet problems but a similar analysis can be developed for other boundary conditions, such as Neumann or Robin.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 6","pages":"Article 125616"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000835/pdfft?md5=7c5aee29b49c6102b8de52d2790f9ff3&pid=1-s2.0-S0723086924000835-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An introduction to pointwise sparse domination 点式稀疏支配导论
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-09-04 DOI: 10.1016/j.exmath.2024.125605
Rodrigo Duarte
{"title":"An introduction to pointwise sparse domination","authors":"Rodrigo Duarte","doi":"10.1016/j.exmath.2024.125605","DOIUrl":"10.1016/j.exmath.2024.125605","url":null,"abstract":"<div><p>The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it allows for a unified approach to proving weighted norm inequalities for a large variety of operators. In this work, we will introduce the basic ideas of dyadic Harmonic Analysis, which we use to build up to the main result we discuss on pointwise sparse domination, which is the Lerner–Ombrosi theorem. We also give applications of this theorem to some families of operators, mainly relating to singular integral operators. The text has been structured so as to motivate the introduction of new ideas through the lens of solving specific problems in Harmonic Analysis.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 6","pages":"Article 125605"},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000720/pdfft?md5=45dd60e1ad35b7a191fa8e59cc8e5e5d&pid=1-s2.0-S0723086924000720-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Digamma function and general Fischer series in the theory of Kempner sums 肯普纳和理论中的迪伽马函数和一般费歇尔级数
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-09-02 DOI: 10.1016/j.exmath.2024.125604
Jean-François Burnol
{"title":"Digamma function and general Fischer series in the theory of Kempner sums","authors":"Jean-François Burnol","doi":"10.1016/j.exmath.2024.125604","DOIUrl":"10.1016/j.exmath.2024.125604","url":null,"abstract":"<div><p>The harmonic sum of the integers which are missing <span><math><mi>p</mi></math></span> given digits in a base <span><math><mi>b</mi></math></span> is expressed as <span><math><mrow><mi>b</mi><mo>log</mo><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>/</mo><mi>p</mi></mrow></math></span> plus corrections indexed by the excluded digits and expressed as integrals involving the digamma function and a suitable measure. A number of consequences are derived, such as explicit bounds, monotony, series representations and asymptotic expansions involving the zeta values at integers, and suitable moments of the measure. In the classic Kempner case of <span><math><mrow><mi>b</mi><mo>=</mo><mn>10</mn></mrow></math></span> and 9 as the only excluded digit, the series representation turns out to be exactly identical with a result obtained by Fischer already in 1993. Extending this work is indeed the goal of the present contribution.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 6","pages":"Article 125604"},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240343","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
Corrigendum to “A simple proof of the Wiener–Ikehara Tauberian Theorem” [Expo. Math. 42 (2024) 125570] 对 "维纳-池原陶伯定理的简单证明 "的更正 [Expo.
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-08-09 DOI: 10.1016/j.exmath.2024.125603
M. Ram Murty , Jagannath Sahoo , Akshaa Vatwani
{"title":"Corrigendum to “A simple proof of the Wiener–Ikehara Tauberian Theorem” [Expo. Math. 42 (2024) 125570]","authors":"M. Ram Murty ,&nbsp;Jagannath Sahoo ,&nbsp;Akshaa Vatwani","doi":"10.1016/j.exmath.2024.125603","DOIUrl":"10.1016/j.exmath.2024.125603","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125603"},"PeriodicalIF":0.8,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000707/pdfft?md5=155e4832fa776ce893a5d10e1db35394&pid=1-s2.0-S0723086924000707-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141963641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recent developments pertaining to Ramanujan’s formula for odd zeta values 拉马努扬奇数zeta值公式的最新进展
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125602
Atul Dixit
{"title":"Recent developments pertaining to Ramanujan’s formula for odd zeta values","authors":"Atul Dixit","doi":"10.1016/j.exmath.2024.125602","DOIUrl":"10.1016/j.exmath.2024.125602","url":null,"abstract":"<div><p>In this expository article, we discuss the contributions made by several mathematicians with regard to a famous formula of Ramanujan for odd zeta values. The goal is to complement the excellent survey by Berndt and Straub (2017) with some of the recent developments that have taken place in the area in the last decade or so.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125602"},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930613","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
A complete Bernstein function related to the fractal dimension of Pascal’s pyramid modulo a prime 与帕斯卡金字塔模数素数分形维度相关的完整伯恩斯坦函数
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-08-02 DOI: 10.1016/j.exmath.2024.125601
Christian Berg
{"title":"A complete Bernstein function related to the fractal dimension of Pascal’s pyramid modulo a prime","authors":"Christian Berg","doi":"10.1016/j.exmath.2024.125601","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125601","url":null,"abstract":"Let for . We prove that is a complete Bernstein function for and a Stieltjes function for . This answers a conjecture of David Bradley that is a Bernstein function when .","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"56 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930603","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
Dicritical foliations and semiroots of plane branches 平面分支的二临界叶形和半根
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-18 DOI: 10.1016/j.exmath.2024.125591
Nuria Corral , Marcelo E. Hernandes , M.E. Rodrigues Hernandes
{"title":"Dicritical foliations and semiroots of plane branches","authors":"Nuria Corral ,&nbsp;Marcelo E. Hernandes ,&nbsp;M.E. Rodrigues Hernandes","doi":"10.1016/j.exmath.2024.125591","DOIUrl":"10.1016/j.exmath.2024.125591","url":null,"abstract":"<div><p>In this work we describe dicritical foliations in <span><math><mrow><mo>(</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> at a triple point of the resolution dual graph of an analytic plane branch <span><math><mi>C</mi></math></span> using its semiroots. In particular, we obtain a constructive method to present a one-parameter family <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of separatrices for such foliations. As a by-product we relate the contact order between a special member of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><mi>C</mi></math></span> with analytic discrete invariants of plane branches.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125591"},"PeriodicalIF":0.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000586/pdfft?md5=3299d7524f5c5d739013dc887d4e9582&pid=1-s2.0-S0723086924000586-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Root involutions, real forms and diagrams 根渐开线、实数形式和图表
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-16 DOI: 10.1016/j.exmath.2024.125593
S. Marini , C. Medori , M. Nacinovich
{"title":"Root involutions, real forms and diagrams","authors":"S. Marini ,&nbsp;C. Medori ,&nbsp;M. Nacinovich","doi":"10.1016/j.exmath.2024.125593","DOIUrl":"10.1016/j.exmath.2024.125593","url":null,"abstract":"<div><p>We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing <span><math><mrow><mi>S</mi><mspace></mspace></mrow></math></span>- and <span><math><mi>Σ</mi></math></span>-<em>diagrams</em>, generalizing those of Satake and Vogan.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125593"},"PeriodicalIF":0.8,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000604/pdfft?md5=445995afea316cbdb564083c3930d697&pid=1-s2.0-S0723086924000604-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative sectional category revisited 重新审视相对断面类别
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-11 DOI: 10.1016/j.exmath.2024.125590
J.M. García-Calcines
{"title":"Relative sectional category revisited","authors":"J.M. García-Calcines","doi":"10.1016/j.exmath.2024.125590","DOIUrl":"10.1016/j.exmath.2024.125590","url":null,"abstract":"<div><p>The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its properties. We seek to uncover how the relative sectional category unifies several homotopic numerical invariants found in recent literature. These include the topological complexity of maps according to Murillo–Wu or Scott, relative topological complexity as defined by Farber, and homotopic distance for continuous maps in the sense of Macías-Virgós and Mosquera-Lois, among others.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125590"},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000574/pdfft?md5=e497014632089ab2358c7bdb9c539959&pid=1-s2.0-S0723086924000574-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On ordinary isogeny graphs with level structures 关于具有水平结构的普通等值图
IF 0.8 4区 数学
Expositiones Mathematicae Pub Date : 2024-07-05 DOI: 10.1016/j.exmath.2024.125589
Antonio Lei , Katharina Müller
{"title":"On ordinary isogeny graphs with level structures","authors":"Antonio Lei ,&nbsp;Katharina Müller","doi":"10.1016/j.exmath.2024.125589","DOIUrl":"10.1016/j.exmath.2024.125589","url":null,"abstract":"<div><p>Let <span><math><mi>ℓ</mi></math></span> and <span><math><mi>p</mi></math></span> be two distinct prime numbers. We study <span><math><mi>ℓ</mi></math></span>-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic <span><math><mi>p</mi></math></span>, together with a level structure. Firstly, we show that as the level varies over all <span><math><mi>p</mi></math></span>-powers, the graphs form an Iwasawa-theoretic abelian <span><math><mi>p</mi></math></span>-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of <span><math><mi>ℓ</mi></math></span>-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125589"},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000562/pdfft?md5=421a5d8db9c34e0de0dd8471dd9d689a&pid=1-s2.0-S0723086924000562-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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