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An existence result in annular regions times conical shells and its application to nonlinear Poisson systems 一个环形区域倍锥壳的存在性结果及其在非线性泊松系统中的应用
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-04-06 DOI: 10.1007/s10231-026-01671-7
Gennaro Infante, Giovanni Mascali, Jorge Rodríguez–López
{"title":"An existence result in annular regions times conical shells and its application to nonlinear Poisson systems","authors":"Gennaro Infante,&nbsp;Giovanni Mascali,&nbsp;Jorge Rodríguez–López","doi":"10.1007/s10231-026-01671-7","DOIUrl":"10.1007/s10231-026-01671-7","url":null,"abstract":"<div>\u0000 \u0000 <p>We provide a new existence result for abstract nonlinear operator systems in normed spaces, by means of topological methods. The solution is located within the product of annular regions and conical shells. The theoretical result possesses a wide range of applicability, which, for concreteness, we illustrate in the context of systems of nonlinear Poisson equations subject to homogeneous Dirichlet boundary conditions. For the latter problem we obtain existence and localization of solutions having all components nontrivial. This is also illustrated with an explicit example in which we also furnish a numerically approximated solution, consistent with the theoretical results. We conclude with an application of our results to a reaction–diffusion Lotka–Volterra system with source terms for competing species.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2287 - 2304"},"PeriodicalIF":0.9,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01671-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628574","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
Asymptotic estimates for the torsional rigidity of rods with thinning cross sections 截面变薄杆抗扭刚度的渐近估计
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-03-09 DOI: 10.1007/s10231-026-01668-2
Alberto Ferrero
{"title":"Asymptotic estimates for the torsional rigidity of rods with thinning cross sections","authors":"Alberto Ferrero","doi":"10.1007/s10231-026-01668-2","DOIUrl":"10.1007/s10231-026-01668-2","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the torsional rigidity for rods with thinning cross sections. The main purpose of the paper is to prove rigorous asymptotic formulas for the torsional rigidity as the thickness of the cross section tends to zero. These asymptotic formulas are empirically known and are widely used in the field of Mechanics of Materials. From a more theoretical point of view, thinning domains are considered when studying optimal inequalities for suitable classes of functionals depending on domains. We recall as an example of this kind of inequalities the celebrated <i>Saint Venant inequality</i> stating that, among planar domains with fixed Lebesgue measure, the disk is the cross section corresponding to a maximal torsional rigidity. It is well known that this statement is equivalent to say that disks are maximizer of a suitable functional, see for example (Amato et al. in On the optimal sets in Pólya and Makai type inequalities, 2025) and the references therein. Actually, in the present paper other kinds of functionals are more relevant when considering thinning domains. We refer in particular to the so-called Pólya and Makai functionals, see the papers (Makai in On the principal frequency of a membrane and the torsional rigidity of a beam, Stanford Univ. Press, Stanford, 1962; Pólya, J Indian Math Soc (N.S.) 24(1960):413–419, 1961; Pólya and Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, 1951) for more details and (1.14) in the present paper for the precise definitions.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"2163 - 2204"},"PeriodicalIF":0.9,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01668-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628626","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
Runge type approximation results for spaces of smooth Whitney jets 光滑惠特尼射流空间的龙格型近似结果
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2026-03-05 DOI: 10.1007/s10231-026-01655-7
Tomasz Ciaś, Thomas Kalmes
{"title":"Runge type approximation results for spaces of smooth Whitney jets","authors":"Tomasz Ciaś,&nbsp;Thomas Kalmes","doi":"10.1007/s10231-026-01655-7","DOIUrl":"10.1007/s10231-026-01655-7","url":null,"abstract":"<div>\u0000 \u0000 <p>We prove Runge type approximation results for linear partial differential operators with constant coefficients on spaces of smooth Whitney jets. Among others, we characterize when for a constant coefficient linear partial differential operator <i>P</i>(<i>D</i>) and for closed subsets <span>(F_1subset F_2)</span> of <span>(mathbb {R}^d)</span> the restrictions to <span>(F_1)</span> of smooth Whitney jets <i>f</i> on <span>(F_2)</span> satisfying <span>(P(D)f=0)</span> on <span>(F_2)</span> are dense in the space of smooth Whitney jets on <span>(F_1)</span> satisfying the same partial differential equation on <span>(F_1)</span>. For elliptic operators we give a geometric evaluation of this characterization. Additionally, for differential operators with a single characteristic direction, like parabolic operators, we give a sufficient geometric condition for the above density to hold. Under mild additional assumptions on <span>(partial F_1)</span> and for <span>(F_2=mathbb {R}^d)</span> this sufficient conditions is also necessary. As an application of our work, we characterize those open subsets <span>(Omega)</span> of the complex plane satisfying <span>(Omega =operatorname {int}overline{Omega })</span> for which the set of holomorphic polynomials are dense in <span>(A^infty (Omega ))</span>, under the additional hypothesis that <span>(overline{Omega })</span> satisfies the strong regularity condition. Furthermore, for the wave operator in one spatial variable, a simple sufficient geometric condition on <span>(F_1, F_2subset mathbb {R}^2)</span> is given for the above density to hold. For the special case of <span>(F_2=mathbb {R}^2)</span> this sufficient condition is also necessary under mild additional hypotheses on <span>(F_1)</span>.</p>\u0000 </div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 4","pages":"1769 - 1797"},"PeriodicalIF":0.9,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01655-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148628573","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
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
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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