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New a Priori estimate for stochastic 2D Navier–Stokes equations with applications to invariant measure 新的二维随机Navier-Stokes方程的先验估计及其在不变测度上的应用
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-11 DOI: 10.1007/s10231-024-01517-0
Matteo Ferrari
{"title":"New a Priori estimate for stochastic 2D Navier–Stokes equations with applications to invariant measure","authors":"Matteo Ferrari","doi":"10.1007/s10231-024-01517-0","DOIUrl":"10.1007/s10231-024-01517-0","url":null,"abstract":"<div><p>The paper deals with the stochastic two-dimensional Navier–Stokes equations for homogeneous and incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form <span>(G,textrm{d}W)</span>, where <i>W</i> is a cylindrical Wiener process and <i>G</i> a bounded linear operator with range dense in the domain of <span>(A^gamma )</span>, <i>A</i> being the Stokes operator. While it is known that existence of invariant measure holds for <span>(gamma &gt;1/4)</span>, previous results show its uniqueness only for <span>(gamma &gt; 3/8)</span>. We fill this gap and prove uniqueness and strong mixing property in the range <span>(gamma in (1/4, 3/8])</span> by adapting the so-called Sobolevskiĭ-Kato-Fujita approach to the stochastic N–S equations. This method provides new <i>a priori</i> estimates, which entail both better regularity in space for the solution and strong Feller and irreducibility properties for the associated Markov semigroup.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1019 - 1051"},"PeriodicalIF":1.0,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930165","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
The limit as (snearrow 1) of the fractional convex envelope 分数阶凸包络的极限为(snearrow 1)
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-11 DOI: 10.1007/s10231-024-01522-3
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas, Julio D. Rossi
{"title":"The limit as (snearrow 1) of the fractional convex envelope","authors":"Begoña Barrios,&nbsp;Leandro M. Del Pezzo,&nbsp;Alexander Quaas,&nbsp;Julio D. Rossi","doi":"10.1007/s10231-024-01522-3","DOIUrl":"10.1007/s10231-024-01522-3","url":null,"abstract":"<div><p>We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of a domain is defined as the largest possible convex function inside the domain that is below the datum on the boundary. Here we prove that the fractional convex envelope inside a strictly convex domain of a continuous and bounded exterior datum converges when <span>(snearrow 1)</span> to the classical convex envelope of the restriction to the boundary of the exterior datum.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1147 - 1160"},"PeriodicalIF":1.0,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930158","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
Some Riemannian properties of (mathbf {SU_n}) endowed with a bi-invariant metric 赋予双不变度规(mathbf {SU_n})的一些黎曼性质
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-07 DOI: 10.1007/s10231-024-01516-1
Donato Pertici, Alberto Dolcetti
{"title":"Some Riemannian properties of (mathbf {SU_n}) endowed with a bi-invariant metric","authors":"Donato Pertici,&nbsp;Alberto Dolcetti","doi":"10.1007/s10231-024-01516-1","DOIUrl":"10.1007/s10231-024-01516-1","url":null,"abstract":"<div><p>We study some properties of <span>(SU_n)</span> endowed with the Frobenius metric <span>(phi )</span>, which is, up to a positive constant multiple, the unique bi-invariant Riemannian metric on <span>(SU_n)</span>. In particular we express the distance between <span>(P, Q in SU_n)</span> in terms of eigenvalues of <span>(P^*Q)</span>; we compute the diameter of <span>((SU_n, phi ))</span> and we determine its diametral pairs; we prove that the set of all minimizing geodesic segments with endpoints <i>P</i>, <i>Q</i> can be parametrized by means of a compact connected submanifold of <span>(mathfrak {su}_n)</span>, diffeomorphic to a suitable complex Grassmannian depending on <i>P</i> and <i>Q</i>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1003 - 1017"},"PeriodicalIF":1.0,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930002","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 a parabolic p-Laplacian system with a convective term 带对流项的抛物型p-拉普拉斯方程组
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-07 DOI: 10.1007/s10231-024-01521-4
Francesca Crispo, Angelica Pia Di Feola
{"title":"On a parabolic p-Laplacian system with a convective term","authors":"Francesca Crispo,&nbsp;Angelica Pia Di Feola","doi":"10.1007/s10231-024-01521-4","DOIUrl":"10.1007/s10231-024-01521-4","url":null,"abstract":"<div><p>We prove a result of existence and a maximum principle for strong solutions, for <span>(t&gt;0)</span>, to a parabolic <i>p</i>-Laplacian system with convective term.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1119 - 1146"},"PeriodicalIF":1.0,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930001","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
Optimizing the first Robin Eigenvalue in exterior domains: the ball’s local maximizing property 优化第一罗宾特征值在外部域：球的局部最大化性质
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-05 DOI: 10.1007/s10231-024-01520-5
Lukas Bundrock
{"title":"Optimizing the first Robin Eigenvalue in exterior domains: the ball’s local maximizing property","authors":"Lukas Bundrock","doi":"10.1007/s10231-024-01520-5","DOIUrl":"10.1007/s10231-024-01520-5","url":null,"abstract":"<div><p>This paper builds upon the work of D. Krejčiřík and V. Lotoreichik, focusing on optimizing the lowest point of the spectrum of the Laplacian in the exterior of a compact set under attractive Robin boundary conditions. We characterize the discrete spectrum of the Laplace operator under Robin boundary conditions using a harmonic Steklov eigenvalue problem in exterior domains. Assuming the lowest point of the spectrum is a discrete eigenvalue, we show that the exterior of a ball is a local maximizer among nearly spherical domains with prescribed measure in any dimension. However, generally, it is not the global maximizer of the first Robin eigenvalue under either prescribed measure or prescribed perimeter.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1095 - 1117"},"PeriodicalIF":1.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929984","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
Needle orientation for temporomandibular joint arthrocentesis in Koreans. 韩国人颞下颌关节关节腔穿刺术的针头方向。
IF 2 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-11-01 Epub Date: 2022-03-09 DOI: 10.1080/08869634.2022.2047509
Atapol Yongvikul, Jae-Young Kim, Jeong-Kui Ku, Joon-Ho Jung, Jong-Ki Huh
{"title":"Needle orientation for temporomandibular joint arthrocentesis in Koreans.","authors":"Atapol Yongvikul, Jae-Young Kim, Jeong-Kui Ku, Joon-Ho Jung, Jong-Ki Huh","doi":"10.1080/08869634.2022.2047509","DOIUrl":"10.1080/08869634.2022.2047509","url":null,"abstract":"<p><strong>Objective: </strong>To investigate the highest opportunity skin puncture point and needle orientation according to facial asymmetry and classification.</p><p><strong>Methods: </strong>Computed tomography of 136 patients was analyzed. Horizontal and vertical angles and distances from the canthal-tragal line were investigated to determine the puncture point and needle's angle.</p><p><strong>Result: </strong>All patients' average points were 7.39 (±2.85) mm anterior to the tragus and 3.44 (±4.18) mm below the canthal-tragal line with an angle of 8.53 (±6.90)° anteriorly and 32.26 (±7.23)° superiorly. Regarding asymmetry, there was a statistical difference in horizontal angle, depth, and canthal-tragal distance between the deviated and non-deviated sides. Especially, vertical distances were 4.44 (±4.66) mm and 2.59 (±4.11) mm in the deviated and non-deviated sides, respectively (<i>p</i> < 0.001).</p><p><strong>Conclusion: </strong>In closed-mouth, the puncture point was closer to the tragus and lower than the conventional point. The point in the deviated side should be considered lower than the non-deviated side.</p>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"51 1","pages":"711-717"},"PeriodicalIF":2.0,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73993630","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
Weakly-monotone (C^*)-algebras as Exel–Laca algebras 弱单调(C^*) -代数作为Exel-Laca代数
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-29 DOI: 10.1007/s10231-024-01519-y
Vitonofrio Crismale, Simone Del Vecchio, Stefano Rossi, Janusz Wysoczański
{"title":"Weakly-monotone (C^*)-algebras as Exel–Laca algebras","authors":"Vitonofrio Crismale,&nbsp;Simone Del Vecchio,&nbsp;Stefano Rossi,&nbsp;Janusz Wysoczański","doi":"10.1007/s10231-024-01519-y","DOIUrl":"10.1007/s10231-024-01519-y","url":null,"abstract":"<div><p>An abstract characterization of weakly monotone <span>(C^*)</span>-algebras, namely the concrete <span>(C^*)</span>-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotients of) suitable Exel–Laca algebras. The weakly monotone <span>(C^*)</span>-algebra indexed by <span>({mathbb N})</span> is shown to be a type-I <span>(C^*)</span>-algebra and its representation theory is entirely determined, whereas the weakly monotone <span>(C^*)</span>-algebra indexed by <span>({mathbb Z})</span> is shown not to be of type <i>I</i>. \u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1075 - 1094"},"PeriodicalIF":1.0,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930193","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
Bergman projection induced by radial weight acting on growth spaces 由作用于生长空间的径向权引起的伯格曼投影
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-24 DOI: 10.1007/s10231-024-01518-z
Álvaro Miguel Moreno, José Ángel Peláez, Jari Taskinen
{"title":"Bergman projection induced by radial weight acting on growth spaces","authors":"Álvaro Miguel Moreno,&nbsp;José Ángel Peláez,&nbsp;Jari Taskinen","doi":"10.1007/s10231-024-01518-z","DOIUrl":"10.1007/s10231-024-01518-z","url":null,"abstract":"<div><p>Let <span>(omega )</span> be a radial weight on the unit disc of the complex plane <span>(mathbb {D})</span> and denote by <span>(widehat{omega }(r)=int _r^1 omega (s),ds)</span> the tail integrals. A radial weight <span>(omega )</span> belongs to the class <span>(widehat{mathcal {D}})</span> if satisfies the upper doubling condition </p><div><div><span>$$begin{aligned} sup _{0&lt;r&lt;1}frac{widehat{omega }(r)}{widehat{omega }left( frac{1+r}{2}right) }&lt;infty . end{aligned}$$</span></div></div><p>If <span>(nu )</span> or <span>(omega )</span> belongs to <span>(widehat{mathcal {D}})</span>, we describe the boundedness of the Bergman projection <span>(P_omega )</span> induced by <span>(omega )</span> on the growth space <span>(L^infty _{widehat{nu }} ={ f: Vert fVert _{infty ,v}=text {ess sup}_{zin mathbb {D}} |f(z)|widehat{nu }(z)&lt;infty })</span> in terms of neat conditions on the moments and/or the tail integrals of <span>(omega )</span> and <span>(nu )</span>. Moreover, we solve the analogous problem for <span>(P_omega )</span> from <span>(L^infty _{widehat{nu }})</span> to the Bloch type space <span>(mathcal {B}^infty _{widehat{nu }} = {f, text {analytic in} mathbb {D}: Vert fVert _{mathcal {B}^infty _{widehat{nu }}} )</span> <span>(= sup _{zin mathbb {D}}(1-|z|)widehat{nu }(z)|f'(z)|&lt;infty }.)</span> Similar questions for exponentially decreasing radial weights will also be studied.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1053 - 1073"},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01518-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929952","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 behavior of fractional Musielak–Orlicz–Sobolev modulars without the (Delta _2)-condition 无(Delta _2) -条件下分数阶Musielak-Orlicz-Sobolev模的渐近行为
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-21 DOI: 10.1007/s10231-024-01515-2
J. C. de Albuquerque, L. R. S. de Assis, M. L. M. Carvalho, A. Salort
{"title":"Asymptotic behavior of fractional Musielak–Orlicz–Sobolev modulars without the (Delta _2)-condition","authors":"J. C. de Albuquerque,&nbsp;L. R. S. de Assis,&nbsp;M. L. M. Carvalho,&nbsp;A. Salort","doi":"10.1007/s10231-024-01515-2","DOIUrl":"10.1007/s10231-024-01515-2","url":null,"abstract":"<div><p>In this article, we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1 without requiring the <span>(Delta _2)</span>-condition on the generalized Young function or its complementary function. This provides a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particular case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"983 - 1002"},"PeriodicalIF":1.0,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930089","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
A generalization of Inoue surfaces (S^+) 井上曲面的推广 (S^+)
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-10-17 DOI: 10.1007/s10231-024-01513-4
David Petcu
{"title":"A generalization of Inoue surfaces (S^+)","authors":"David Petcu","doi":"10.1007/s10231-024-01513-4","DOIUrl":"10.1007/s10231-024-01513-4","url":null,"abstract":"<div><p>Using Lie groups with left-invariant complex structure, we construct new examples of compact complex manifolds with flat affine structure in arbitrarly high dimensions. In the 2-dimensional case, we retrieve the Inoue surfaces <span>(S^+)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"943 - 960"},"PeriodicalIF":1.0,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01513-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930058","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
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