Annali di Matematica Pura ed Applicata最新文献

On the microlocal regularity of the Gevrey vectors for second order partial differential operators with non negative characteristic form of first kind 一类非负特征形式二阶偏微分算子Gevrey向量的微局部正则性

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-08-10 DOI: 10.1007/s10231-026-01698-w

Gregorio Chinni, Makhlouf Derridj

{"title":"On the microlocal regularity of the Gevrey vectors for second order partial differential operators with non negative characteristic form of first kind","authors":"Gregorio Chinni, Makhlouf Derridj","doi":"10.1007/s10231-026-01698-w","DOIUrl":"10.1007/s10231-026-01698-w","url":null,"abstract":"<div>We study the microlocal regularity of the analytic/Gevrey vectors for the following class of second order partial differential equations <div><div>$$begin{aligned} P(x,D) = sum _{ell ,j=1}^{n} a_{ell ,j}(x) D_{ell } D_{j} + sum _{ell =1}^{n} i b_{ell }(x) D_{ell } +c(x), end{aligned}$$</div></div>where (a_{ell ,j}(x) = a_{j,ell }(x)), (b_{ell }(x)), (ell ,j in lbrace 1,dots ,, nrbrace ), are real valued real Gevrey functions of order s and c(x) is a Gevrey function of order s, (s ge 1), on (Omega ) open neighborhood of the origin in ({mathbb {R}}^{n}). Thus providing a microlocal version of a result due to Derridj in (Complex Anal. Synerg. 6:10, 2020). The class of operators considered in this work generalizes the classes studied by Braun Rodrigues-Chinni-Cordaro-Jahnke (Proc. Am. Math. Soc. 144:5159–5170, 2016) and Chinni-Derridj (Math. Z. 302:1983–2003, 2022).</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 6","pages":"3053 - 3110"},"PeriodicalIF":0.9,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01698-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149309802","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

Reflections and Drinfeld twists for set-theoretic Yang–Baxter maps 集论Yang-Baxter映射的反射和Drinfeld扭曲

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-07-13 DOI: 10.1007/s10231-026-01703-2

Davide Ferri

{"title":"Reflections and Drinfeld twists for set-theoretic Yang–Baxter maps","authors":"Davide Ferri","doi":"10.1007/s10231-026-01703-2","DOIUrl":"10.1007/s10231-026-01703-2","url":null,"abstract":"<div>The Yang–Baxter equation (ybe) and the reflection equation (re) both come from mathematical physics, and they can be defined in any monoidal category. For cartesian monoidal categories, we prove that every solution to the re provides a Drinfeld twist for a solution of the ybe. As we observe, Drinfeld twists of solutions are relevant for the following reason: two solutions to the ybe (in any strict monoidal category) are related by a Drinfeld twist, if and only if they induce equivalent representations of the braid group. In the category of sets, it is known that every solution is associated with a structure group, which is a braided group in the sense of Lu et al. (Duke Math J 104(1):1–18, 2000). Using De Commer’s notion of a braided action, we then define group reflections for a braided group. We prove that group reflections provide group Drinfeld twists in the sense of Ghobadi. Finally, we characterise when a reflection on a solution (X, r) can be extended to a group reflection on its structure group G(X, r).</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 6","pages":"3213 - 3243"},"PeriodicalIF":0.9,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01703-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149309593","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

Boundary regularity for parabolic systems with nonstandard (p,q)-growth conditions in smooth convex domains 光滑凸域上具有非标准（p,q）生长条件的抛物型系统的边界正则性

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-06-23 DOI: 10.1007/s10231-026-01708-x

Michael Strunk

引用次数: 0

Robustness and dichotomy radii for discrete dynamics on the half-line 半线上离散动力学的鲁棒性和二分半径

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-06-18 DOI: 10.1007/s10231-026-01710-3

Davor Dragičević, Adina Luminiţa Sasu, Bogdan Sasu

{"title":"Robustness and dichotomy radii for discrete dynamics on the half-line","authors":"Davor Dragičević, Adina Luminiţa Sasu, Bogdan Sasu","doi":"10.1007/s10231-026-01710-3","DOIUrl":"10.1007/s10231-026-01710-3","url":null,"abstract":"<div>We present a complete study on the dichotomy roughness and dichotomy radii for nonautonomous discrete dynamics on the half-line, in infinite-dimensional spaces. Our approach is based on new characterizations of the uniform exponential dichotomy that extend the results in [72]. We prove novel criteria for the robustness of the uniform exponential dichotomy, providing general bounds for the perturbations that preserve it. We introduce for the first time the notions of dichotomy radius on the half-line and of dichotomy radius relative to a subspace and obtain lower bounds for both of these radii. Furthermore, we determine an interval in which the dichotomy radius relative to an unstable subspace varies, expressed in terms of input–output operators. Using explicit examples, we show that the bounds and the dichotomy radii can be calculated, and in certain cases these radii may coincide. All the results are obtained in the most general framework, without imposing any additional hypotheses on the coefficients of the original or perturbed systems or on their propagators.</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 6","pages":"3365 - 3406"},"PeriodicalIF":0.9,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01710-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149310320","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

A Talenti comparison result for a weighted Poisson equation with Neumann boundary value 具有Neumann边值的加权泊松方程的Talenti比较结果

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-06-08 DOI: 10.1007/s10231-026-01711-2

Yifei Dai, Xiaomei Sun, Anqiang Zhu

引用次数: 0

Singular Riemannian foliations, variational problems and principles of symmetric criticalities 奇异黎曼叶，变分问题和对称临界原理

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-26 DOI: 10.1007/s10231-026-01679-z

Marcos M. Alexandrino, Leonardo F. Cavenaghi, Diego Corro, Marcelo K. Inagaki

{"title":"Singular Riemannian foliations, variational problems and principles of symmetric criticalities","authors":"Marcos M. Alexandrino, Leonardo F. Cavenaghi, Diego Corro, Marcelo K. Inagaki","doi":"10.1007/s10231-026-01679-z","DOIUrl":"10.1007/s10231-026-01679-z","url":null,"abstract":"<div>A singular foliation (mathscr {F}) on a complete Riemannian manifold M is called a Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of M into the orbits of a Lie group action by isometries. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRFs with special properties, which we name as AVP. Examples of such SRFs being considered include isoparametric foliations, SRFs on Euclidean fiber bundles, and the partition of M into the orbits of a Lie group acting by isometries. More precisely, we prove an analog to Palais’ Principle of Symmetric Criticality for (mathscr {F})-symmetric integral operators on the Banach spaces (W^{1,p}(M).) This result together with a version of the Rellich–Kondrachov–Hebey–Vaugon Embedding Theorem for (mathscr {F})-basic Sobolev functions allows us to circumvent difficulties with Sobolev’s critical exponents when considering applications of techniques from Calculus of Variations to find solutions to PDEs. To exemplify this, we prove the existence of countably infinite many weak solutions to a class of variational problems, which includes p-Kirchhoff problems for manifolds equipped with an AVP foliation.</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 5","pages":"2507 - 2572"},"PeriodicalIF":0.9,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01679-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176894","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

Correction to: The rigidity of biconservative surfaces in Sol3 修正为：Sol3中双保守表面的刚性

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-21 DOI: 10.1007/s10231-026-01707-y

Dorel Fetcu

引用次数: 0

A family of stochastic pre-orders based on the usual stochastic order 基于通常随机顺序的一组随机预购顺序

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-20 DOI: 10.1007/s10231-026-01706-z

Francesco Buono, Maria Longobardi

引用次数: 0

On the period map of planar Hamiltonian systems with separated variables 带分离变量的平面哈密顿系统的周期映射

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-16 DOI: 10.1007/s10231-026-01709-w

Alessandro Fonda, Maurizio Garrione, Andrea Sfecci

引用次数: 0

Symmetry breaking in biharmonic equations with weighted exponential nonlinearities 加权指数非线性双调和方程的对称性破缺

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2026-05-15 DOI: 10.1007/s10231-026-01700-5

Marta Calanchi, Cristina Tarsi

{"title":"Symmetry breaking in biharmonic equations with weighted exponential nonlinearities","authors":"Marta Calanchi, Cristina Tarsi","doi":"10.1007/s10231-026-01700-5","DOIUrl":"10.1007/s10231-026-01700-5","url":null,"abstract":"<div>We investigate a class of fourth-order elliptic problems involving exponential-type nonlinearities and spatial weights of Hénon type. Motivated by the symmetry-breaking phenomena observed in semilinear second-order problems—such as those governed by the Hénon equation—we consider weighted functionals of the form <div><div>$$begin{aligned} F_m(u) = int _B |x|^alpha left( e^{sigma |u|^2} - sum _{k=0}^m frac{sigma ^k}{k!} |u|^{2k} right) dx, end{aligned}$$</div></div>defined on the unit ball ( B subset mathbb {R}^4 ), where (min mathbb N_0) ( alpha > 0 ), ( sigma >0) are suitable parameters. We first establish an Adams-type inequality with weight, characterizing the sharp threshold for the boundedness of ( F ) on the unit sphere of the biharmonic Sobolev space. Then, we prove that for large values of the weight exponent ( alpha ), radial symmetry of maximizers is broken. These results extend classical findings in the second-order setting (e.g., Trudinger–Moser-type functionals and the weighted Hénon equation) to the biharmonic context and offer new insights into the interplay between weights, nonlinearity, and symmetry in higher-order PDEs.</div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 6","pages":"3155 - 3178"},"PeriodicalIF":0.9,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-026-01700-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149310068","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