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Complete classification of planar p-elasticae 平面 p-elasticae 的完整分类
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-04-01 DOI: 10.1007/s10231-024-01445-z
Tatsuya Miura, Kensuke Yoshizawa
{"title":"Complete classification of planar p-elasticae","authors":"Tatsuya Miura,&nbsp;Kensuke Yoshizawa","doi":"10.1007/s10231-024-01445-z","DOIUrl":"10.1007/s10231-024-01445-z","url":null,"abstract":"<div><p>Euler’s elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its <span>(L^p)</span>-counterpart is called <i>p</i>-elastica. In this paper we completely classify all <i>p</i>-elasticae in the plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new types of <i>p</i>-elliptic functions which streamline the whole argument and result. As an application we also classify all closed planar <i>p</i>-elasticae.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888167","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
Homogenization of fundamental solutions for parabolic operators involving non-self-similar scales 涉及非自相似尺度的抛物线算子基本解的同质化
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-04-01 DOI: 10.1007/s10231-024-01446-y
Qing Meng, Weisheng Niu
{"title":"Homogenization of fundamental solutions for parabolic operators involving non-self-similar scales","authors":"Qing Meng,&nbsp;Weisheng Niu","doi":"10.1007/s10231-024-01446-y","DOIUrl":"10.1007/s10231-024-01446-y","url":null,"abstract":"<div><p>We establish the asymptotic expansion of the fundamental solutions with precise error estimates for second-order parabolic operators </p><div><div><span>$$begin{aligned} partial _t -text {div}(A(x/varepsilon , t/varepsilon ^ell )nabla ), quad , 0&lt;varepsilon&lt;1,, 0&lt;ell &lt;infty ,end{aligned}$$</span></div></div><p>in the case <span>(ell ne 2,)</span> where the spatial and temporal variables oscillate on non-self-similar scales and do not homogenize simultaneously. To achieve the goal, we explore the direct quantitative two-scale expansions for the aforementioned operators, which should be of some independent interests in quantitative homogenization of parabolic operators involving multiple scales. In the self-similar case <span>(ell =2)</span>, similar results have been obtained in Geng and Shen (Anal PDE 13(1): 147–170, 2020).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887835","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
Stability of the Gaussian Faber–Krahn inequality 高斯法布尔-克拉恩不等式的稳定性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-30 DOI: 10.1007/s10231-024-01441-3
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara
{"title":"Stability of the Gaussian Faber–Krahn inequality","authors":"Alessandro Carbotti,&nbsp;Simone Cito,&nbsp;Domenico Angelo La Manna,&nbsp;Diego Pallara","doi":"10.1007/s10231-024-01441-3","DOIUrl":"10.1007/s10231-024-01441-3","url":null,"abstract":"<div><p>We prove a quantitative version of the Gaussian Faber–Krahn type inequality proved in (Betta et al. in Z. Angew. Math. Phys. 58:37–52, 2007) for the first Dirichlet eigenvalue of the Ornstein–Uhlenbeck operator, estimating the deficit in terms of the Gaussian Fraenkel asymmetry. As expected, the multiplicative constant only depends on the prescribed Gaussian measure.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01441-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140361947","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
Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes 新陈代谢过程中带有波纹边界的薄域中的非线性耦合系统
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-29 DOI: 10.1007/s10231-024-01442-2
Giuseppe Cardone, Luisa Faella, Jean Carlos Nakasato, Carmen Perugia
{"title":"Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes","authors":"Giuseppe Cardone,&nbsp;Luisa Faella,&nbsp;Jean Carlos Nakasato,&nbsp;Carmen Perugia","doi":"10.1007/s10231-024-01442-2","DOIUrl":"10.1007/s10231-024-01442-2","url":null,"abstract":"<div><p>In this paper, we study the asymptotic behaviour of solutions of a coupled system of partial differential equations in a thin domain with oscillating boundary and varying order of thickness. In such a thin domain, our model describes the solute concentration of two different biochemical species (metabolites). The coupling between the concentrations of the metabolites is realized through reaction terms even nonlinear, appearing on the oscillating upper wall. Moreover nonlinear reaction terms appear also in the thin domain. The reaction catalyzed by the upper wall is simulated by a Robin-type boundary condition depending on a small parameter <span>(varepsilon )</span>. Hence, taking into account that <span>(alpha &gt;1)</span> and <span>(beta &gt;0)</span>, we analyze the coupled system by comparing the magnitude of the reaction coefficient <span>(varepsilon ^beta )</span> on the upper boundary with the compression order of our thin domain, which can be <span>(varepsilon )</span> or <span>(varepsilon ^alpha )</span>, depending on the sub-regions with different order of thickness. Comparing the exponents 1, <span>(alpha )</span> and <span>(beta )</span>, we obtain different cases for the limit problem which could appear coupled or uncoupled and allow us to identify the effects of the geometry and the physical process on the problem. Moreover it arises a critical value, i.e.<span>(beta =alpha -2)</span>, leading the reaction effects entering in the diffusion matrix.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366902","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
Optimal and typical (L^2) discrepancy of 2-dimensional lattices 二维网格的最佳和典型 $$L^2$ 差异
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-23 DOI: 10.1007/s10231-024-01440-4
Bence Borda
{"title":"Optimal and typical (L^2) discrepancy of 2-dimensional lattices","authors":"Bence Borda","doi":"10.1007/s10231-024-01440-4","DOIUrl":"10.1007/s10231-024-01440-4","url":null,"abstract":"<div><p>We undertake a detailed study of the <span>(L^2)</span> discrepancy of 2-dimensional Korobov lattices and their irrational analogues, either with or without symmetrization. We give a full characterization of such lattices with optimal <span>(L^2)</span> discrepancy in terms of the continued fraction partial quotients, and compute the precise asymptotics whenever the continued fraction expansion is explicitly known, such as for quadratic irrationals or Euler’s number <i>e</i>. In the metric theory, we find the asymptotics of the <span>(L^2)</span> discrepancy for almost every irrational, and the limit distribution for randomly chosen rational and irrational lattices.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01440-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140211176","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 note on p-Kähler structures on compact quotients of Lie groups 李群紧凑商上的 p-Kähler 结构注释
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-21 DOI: 10.1007/s10231-024-01438-y
Anna Fino, Asia Mainenti
{"title":"A note on p-Kähler structures on compact quotients of Lie groups","authors":"Anna Fino,&nbsp;Asia Mainenti","doi":"10.1007/s10231-024-01438-y","DOIUrl":"10.1007/s10231-024-01438-y","url":null,"abstract":"<div><p>A <i>p</i>-Kähler structure on a complex manifold of complex dimension <i>n</i> is given by a <i>d</i>-closed transverse real (<i>p</i>, <i>p</i>)-form. In the paper, we study the existence of <i>p</i>-Kähler structures on compact quotients of simply connected Lie groups by discrete subgroups endowed with an invariant complex structure. In particular, we discuss the existence of <i>p</i>-Kähler structures on nilmanifolds, with a focus on the case <span>(p =2)</span> and complex dimension <span>(n = 4)</span>. Moreover, we prove that a <span>((n-2))</span>-Kähler almost abelian solvmanifold of complex dimension <span>(nge 3)</span> has to be Kähler.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01438-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140221049","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
Relaxed area of 0-homogeneous maps in the strict BV-convergence 严格 BV 收敛中 0 均质映射的松弛区域
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-16 DOI: 10.1007/s10231-024-01435-1
Simone Carano
{"title":"Relaxed area of 0-homogeneous maps in the strict BV-convergence","authors":"Simone Carano","doi":"10.1007/s10231-024-01435-1","DOIUrl":"10.1007/s10231-024-01435-1","url":null,"abstract":"<div><p>We compute the relaxed Cartesian area for a general 0-homogeneous map of bounded variation, with respect to the strict <i>BV</i>-convergence. In particular, we show that the relaxed area is finite for this class of maps and we provide an integral representation formula.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881520","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
Descent of tautological sheaves from Hilbert schemes to Enriques manifolds 从希尔伯特方案到恩里克流形的同调卷的后裔
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-15 DOI: 10.1007/s10231-024-01437-z
Fabian Reede
{"title":"Descent of tautological sheaves from Hilbert schemes to Enriques manifolds","authors":"Fabian Reede","doi":"10.1007/s10231-024-01437-z","DOIUrl":"10.1007/s10231-024-01437-z","url":null,"abstract":"<div><p>Let <i>X</i> be a K3 surface which doubly covers an Enriques surface <i>S</i>. If <span>(nin {mathbb {N}})</span> is an odd number, then the Hilbert scheme of <i>n</i>-points <span>(X^{[n]})</span> admits a natural quotient <span>(S_{[n]})</span>. This quotient is an Enriques manifold in the sense of Oguiso and Schröer. In this paper we construct slope stable sheaves on <span>(S_{[n]})</span> and study some of their properties.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01437-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881515","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 the obstacle problem associated to the Kolmogorov–Fokker–Planck operator with rough coefficients 关于与具有粗糙系数的科尔莫戈罗夫-福克-普朗克算子相关的障碍问题
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-14 DOI: 10.1007/s10231-024-01431-5
Francesca Anceschi, Annalaura Rebucci
{"title":"On the obstacle problem associated to the Kolmogorov–Fokker–Planck operator with rough coefficients","authors":"Francesca Anceschi,&nbsp;Annalaura Rebucci","doi":"10.1007/s10231-024-01431-5","DOIUrl":"10.1007/s10231-024-01431-5","url":null,"abstract":"<div><p>This work is devoted to the study of the obstacle problem associated to the Kolmogorov–Fokker–Planck operator with rough coefficients through a variational approach. In particular, after the introduction of a proper anisotropic Sobolev space and related properties, we prove the existence and uniqueness of a weak solution for the obstacle problem by adapting a classical perturbation argument to the convex functional associated to the case of our interest. Finally, we conclude this work by providing a one-sided associated variational inequality, alongside with an overview on related open problems.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01431-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881535","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
Rotational Ricci surfaces 旋转里奇曲面
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-03-12 DOI: 10.1007/s10231-024-01436-0
Iury Domingos, Roney Santos, Feliciano Vitório
{"title":"Rotational Ricci surfaces","authors":"Iury Domingos,&nbsp;Roney Santos,&nbsp;Feliciano Vitório","doi":"10.1007/s10231-024-01436-0","DOIUrl":"10.1007/s10231-024-01436-0","url":null,"abstract":"<div><p>We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature <i>K</i> satisfies </p><div><div><span>$$begin{aligned} KDelta K - Vert nabla KVert ^2-4K^3 = 0. end{aligned}$$</span></div></div><p>These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881326","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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