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Hopf formulae for cocommutative Hopf algebras 可交换Hopf代数的Hopf公式
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-03-05 DOI: 10.1007/s10231-026-01665-5
Marino Gran, Andrea Sciandra
{"title":"Hopf formulae for cocommutative Hopf algebras","authors":"Marino Gran,&nbsp;Andrea Sciandra","doi":"10.1007/s10231-026-01665-5","DOIUrl":"10.1007/s10231-026-01665-5","url":null,"abstract":"<div>\u0000 \u0000 <p>The adjunction between coalgebras and Hopf algebras, first described by Takeuchi, allows one to prove that the semi-abelian category of cocommutative Hopf algebras has enough <span>(mathcal {E})</span>-projective objects, where <span>(mathcal {E})</span> is the class of cleft extensions. One then proves that, for any cocommutative Hopf algebra, there exists a weak <span>(mathcal {E})</span>-universal normal (=central) extension. This fact allows one to apply the methods of categorical Galois theory to classify normal <span>(mathcal {E})</span>-extensions and to provide an explicit description of the fundamental group of a cocommutative Hopf algebra in terms of a generalized Hopf formula. Moreover, with any cleft extension, we associate a 5-term exact homology sequence that can be seen as a Hopf-theoretic analogue of the classical Stallings-Stammbach exact sequence in group theory.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2073 - 2098"},"PeriodicalIF":0.9,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 energy decay estimates for weak dissipative wave equations with oscillating time-dependent coefficient in the dissipative term 耗散项含时变系数振荡的弱耗散波方程的能量衰减估计
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-03-02 DOI: 10.1007/s10231-026-01677-1
Fumihiko Hirosawa, Daichi Nakajima
{"title":"On energy decay estimates for weak dissipative wave equations with oscillating time-dependent coefficient in the dissipative term","authors":"Fumihiko Hirosawa,&nbsp;Daichi Nakajima","doi":"10.1007/s10231-026-01677-1","DOIUrl":"10.1007/s10231-026-01677-1","url":null,"abstract":"<div>\u0000 \u0000 <p>It is known that the asymptotic behavior of time-dependent dissipative coefficient in the Cauchy problem of dissipative wave equation dominates the energy decay estimate. In particular, it is important to study the case where the dissipative coefficient behaves like 1/<i>t</i> as <i>t</i> goes to infinity, which is called weak dissipation, because its order is close to the critical case of decay and non-decay. In this case, an oscillating perturbation of weak dissipation can give a crucial effect on the energy decay estimate, but the analysis is very difficult compared to the case without oscillations. In this paper, we develop a method recently introduced by Ghisi-Gobbino that has contributed to a precise analysis for dissipative wave equations with oscillating weak dissipation, and consider the effect of the oscillations, which is more general and close to the critical case. Furthermore, we study the effect of the smoothness of the initial data on the energy decay estimates.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2433 - 2471"},"PeriodicalIF":0.9,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Bourgain–Brezis–Mironescu formula for magnetic fractional Sobolev spaces with variable exponents 变指数磁分数Sobolev空间的Bourgain-Brezis-Mironescu公式
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-24 DOI: 10.1007/s10231-026-01673-5
Rosa Lorenzo, Pablo Ochoa, Analía Silva
{"title":"Bourgain–Brezis–Mironescu formula for magnetic fractional Sobolev spaces with variable exponents","authors":"Rosa Lorenzo,&nbsp;Pablo Ochoa,&nbsp;Analía Silva","doi":"10.1007/s10231-026-01673-5","DOIUrl":"10.1007/s10231-026-01673-5","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we state the so-called Bourgain–Brezis–Mironescu formula in the setting of magnetic fractional Sobolev spaces with variable exponents. To the best of our knowledge, this is the first time that these spaces are considered. We also show that, unlike the constant-power case, there are functions in the limiting space for which the BBM formula does not hold. Moreover, we define a generalization of the Schrödinger operator related to the magnetic energy functional with variable exponents.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2349 - 2367"},"PeriodicalIF":0.9,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Second-order boundary estimates for solutions to a class of quasilinear elliptic equations 一类拟线性椭圆方程解的二阶边界估计
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-23 DOI: 10.1007/s10231-026-01672-6
Giuseppe Spadaro, Domenico Vuono
{"title":"Second-order boundary estimates for solutions to a class of quasilinear elliptic equations","authors":"Giuseppe Spadaro,&nbsp;Domenico Vuono","doi":"10.1007/s10231-026-01672-6","DOIUrl":"10.1007/s10231-026-01672-6","url":null,"abstract":"<div>\u0000 \u0000 <p>We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2305 - 2347"},"PeriodicalIF":0.9,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01672-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Complete normal forms for real hypersurfaces in (mathbb {C}^3) at 2-nondegenerate points of Levi non-uniform rank zero (mathbb {C}^3)中李维非均匀秩为零的2-非简并点上的实超曲面的完备范式
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-23 DOI: 10.1007/s10231-026-01666-4
Masoud Sabzevari
{"title":"Complete normal forms for real hypersurfaces in (mathbb {C}^3) at 2-nondegenerate points of Levi non-uniform rank zero","authors":"Masoud Sabzevari","doi":"10.1007/s10231-026-01666-4","DOIUrl":"10.1007/s10231-026-01666-4","url":null,"abstract":"<div>\u0000 \u0000 <p>We construct <i>complete</i> normal forms for 5-dimensional real hypersurfaces in <span>(mathbb {C}^3)</span> which are 2-nondegenerate and also of Levi non-uniform rank zero at the origin point <span>({varvec{p}}=0)</span>. The latter condition means that the rank of the Levi form vanishes at <span>({varvec{p}})</span> but not identically in a neighborhood of it. The mentioned hypersurfaces are the only finitely nondegenerate real hypersurfaces in <span>(mathbb {C}^3)</span> for which their complete normal forms were absent in the literature. As a byproduct, we also treat the underlying biholomorphic equivalence problem between the hypersurfaces. Our primary approach in constructing the desired complete normal forms is to utilize the techniques derived in the theory of equivariant moving frames. It notably offers the advantage of systematic and symbolic manipulation of the associated computations.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2099 - 2138"},"PeriodicalIF":0.9,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Parabolic problems for direction-dependent local–nonlocal operators 方向相关局部-非局部算子的抛物问题
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-21 DOI: 10.1007/s10231-026-01669-1
Jamil Chaker, Moritz Kassmann, Marvin Weidner
{"title":"Parabolic problems for direction-dependent local–nonlocal operators","authors":"Jamil Chaker,&nbsp;Moritz Kassmann,&nbsp;Marvin Weidner","doi":"10.1007/s10231-026-01669-1","DOIUrl":"10.1007/s10231-026-01669-1","url":null,"abstract":"<div>\u0000 \u0000 <p>We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting contains the purely nonlocal, as well as the purely local case. Our approach is based on an energy method allowing for jumping measures that are singular or supported on cusps. In addition, the jumping measure may depend on the direction. The emphasis of our study is on the weak Harnack inequality and Hölder regularity estimates for solutions of such equations. The main regularity estimates are robust in the sense that the constants can be chosen independently of the order of differentiability of the operators.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2205 - 2258"},"PeriodicalIF":0.9,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01669-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 (mathfrak {P})-adic continued fractions with extraneous denominators: some explicit finiteness results 关于(mathfrak {P})带外分母的进位连分数：一些显式的有限结果
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-20 DOI: 10.1007/s10231-026-01670-8
Laura Capuano, Sara Checcoli, Marzio Mula, Lea Terracini
{"title":"On (mathfrak {P})-adic continued fractions with extraneous denominators: some explicit finiteness results","authors":"Laura Capuano,&nbsp;Sara Checcoli,&nbsp;Marzio Mula,&nbsp;Lea Terracini","doi":"10.1007/s10231-026-01670-8","DOIUrl":"10.1007/s10231-026-01670-8","url":null,"abstract":"<div><p>Let <i>K</i> be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for <span>(mathfrak {P})</span>-adic continued fractions satisfying the finiteness property on <i>K</i> for every prime ideal <span>(mathfrak {P})</span> of sufficiently large norm. This provides, in particular, a new algorithmic approach to the construction of division chains in number fields.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2259 - 2286"},"PeriodicalIF":0.9,"publicationDate":"2026-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01670-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients 系数可测非线性x -椭圆方程解的存在性和可求和性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-14 DOI: 10.1007/s10231-026-01667-3
Marco Picerni
{"title":"Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients","authors":"Marco Picerni","doi":"10.1007/s10231-026-01667-3","DOIUrl":"10.1007/s10231-026-01667-3","url":null,"abstract":"<div>\u0000 \u0000 <p>We prove an existence result for solutions to a class of nonlinear degenerate elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form associated to a family of vector fields which satisfy a Poincaré inequality and the doubling condition. Furthermore, we prove that the solutions satisfy a generalization of the <span>(L^p)</span>-regularity results which hold for the solutions to Leray–Lions type equations.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2139 - 2162"},"PeriodicalIF":0.9,"publicationDate":"2026-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01667-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-singular geodesic orbit nilmanifolds 非奇异测地线轨道零流形
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-10 DOI: 10.1007/s10231-026-01661-9
Y. Nikolayevsky, W. Ziller
{"title":"Non-singular geodesic orbit nilmanifolds","authors":"Y. Nikolayevsky,&nbsp;W. Ziller","doi":"10.1007/s10231-026-01661-9","DOIUrl":"10.1007/s10231-026-01661-9","url":null,"abstract":"<div><p>A Riemannian manifold is called a <i>geodesic orbit</i> manifold, GO for short, if any geodesic is an orbit of a one-parameter group of isometries. By a result of C.Gordon, a non-flat GO nilmanifold is necessarily a two-step nilpotent Lie group with a left-invariant metric. We give a complete classification of non-singular GO nilmanifolds. Besides previously known examples, there are new families with 3-dimensional center, and two one-parameter families of dimensions 14 and 15.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1939 - 1973"},"PeriodicalIF":0.9,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01661-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Partially concentrating solutions for systems with Lotka–Volterra type interactions 具有Lotka-Volterra型相互作用的系统的部分集中解
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-02-10 DOI: 10.1007/s10231-026-01662-8
Sabrina Caputo, Giusi Vaira
{"title":"Partially concentrating solutions for systems with Lotka–Volterra type interactions","authors":"Sabrina Caputo,&nbsp;Giusi Vaira","doi":"10.1007/s10231-026-01662-8","DOIUrl":"10.1007/s10231-026-01662-8","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper we consider the existence of standing waves for a coupled system of <i>k</i> equations with Lotka–Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the <span>(k-1)</span>-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka–Volterra type systems.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1975 - 2019"},"PeriodicalIF":0.9,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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