Annali di Matematica Pura ed Applicata最新文献

{"title":"Variational inequality solutions and finite stopping time for a class of shear-thinning flows","authors":"Laurent Chupin,&nbsp;Nicolae Cîndea,&nbsp;Geoffrey Lacour","doi":"10.1007/s10231-024-01457-9","DOIUrl":"10.1007/s10231-024-01457-9","url":null,"abstract":"<div><p>The aim of this paper is to study the existence of a finite stopping time for solutions in the form of variational inequality to fluid flows following a power law (or Ostwald–DeWaele law) in dimension <span>(N in {2,3})</span>. We first establish the existence of solutions for generalized Newtonian flows, valid for viscous stress tensors associated with the usual laws such as Ostwald–DeWaele, Carreau–Yasuda, Herschel–Bulkley and Bingham, but also for cases where the viscosity coefficient satisfies a more atypical (logarithmic) form. To demonstrate the existence of such solutions, we proceed by applying a nonlinear Galerkin method with a double regularization on the viscosity coefficient. We then establish the existence of a finite stopping time for threshold fluids or shear-thinning power-law fluids, i.e. formally such that the viscous stress tensor is represented by a <i>p</i>-Laplacian for the symmetrized gradient for <span>(p in [1,2))</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881533","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}

{"title":"Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge","authors":"Erasmo Caponio,&nbsp;Dario Corona,&nbsp;Roberto Giambò,&nbsp;Paolo Piccione","doi":"10.1007/s10231-024-01424-4","DOIUrl":"10.1007/s10231-024-01424-4","url":null,"abstract":"<div><p>We consider an autonomous, indefinite Lagrangian <i>L</i> admitting an infinitesimal symmetry <i>K</i> whose associated Noether charge is linear in each tangent space. Our focus lies in investigating solutions to the Euler-Lagrange equations having fixed energy and that connect a given point <i>p</i> to a flow line <span>(gamma =gamma (t))</span> of <i>K</i> that does not cross <i>p</i>. By utilizing the invariance of <i>L</i> under the flow of <i>K</i>, we simplify the problem into a two-point boundary problem. Consequently, we derive an equation that involves the differential of the “arrival time” <i>t</i>, seen as a functional on the infinite dimensional manifold of connecting paths satisfying the semi-holonomic constraint defined by the Noether charge. When <i>L</i> is positively homogeneous of degree 2 in the velocities, the resulting equation establishes a variational principle that extends the Fermat’s principle in a stationary spacetime. Furthermore, we also analyze the scenario where the Noether charge is affine.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01424-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805224","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}

{"title":"Polyharmonic hypersurfaces into complex space forms","authors":"José Miguel Balado-Alves","doi":"10.1007/s10231-024-01452-0","DOIUrl":"10.1007/s10231-024-01452-0","url":null,"abstract":"<div><p>We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for <span>(mathbb{C}mathbb{P}^n)</span> and <span>(mathbb{C}mathbb{H}^n)</span>, respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01452-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881691","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}

{"title":"On CLT and non-CLT groups","authors":"Marius Tărnăuceanu","doi":"10.1007/s10231-024-01450-2","DOIUrl":"10.1007/s10231-024-01450-2","url":null,"abstract":"<div><p>In this note, we prove that for every integer <span>(dge 2)</span> which is not a prime power, there exists a finite solvable group <i>G</i> such that <span>(dmid |G|)</span>, <span>(pi (G)=pi (d))</span> and <i>G</i> has no subgroup of order <i>d</i>. We also introduce the CLT-degree of a finite group and answer two questions about it.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881517","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}

{"title":"Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals","authors":"Pierre Bousquet,&nbsp;Carlo Mariconda,&nbsp;Giulia Treu","doi":"10.1007/s10231-024-01444-0","DOIUrl":"10.1007/s10231-024-01444-0","url":null,"abstract":"<div><p>We consider a multidimensional scalar problem of the calculus of variations with a nonnegative general Lagrangian depending on the space variable, on a Sobolev function and on its gradient. The main result of the paper is a sufficient condition discarding the Lavrentiev phenomenon between Sobolev and Lipschitz functions, with a prescribed boundary datum. The result unifies most of the known conditions in the literature and does not require that the Lagrangian obey a <i>p</i>-<i>q</i> growth condition or be an <i>N</i>-function.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140708646","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}

{"title":"Locally conformally product structures on solvmanifolds","authors":"Adrián Andrada,&nbsp;Viviana del Barco,&nbsp;Andrei Moroianu","doi":"10.1007/s10231-024-01449-9","DOIUrl":"10.1007/s10231-024-01449-9","url":null,"abstract":"<div><p>We study left invariant locally conformally product structures on simply connected Lie groups and give their complete description in the solvable unimodular case. Based on previous classification results, we then obtain the complete list of solvable unimodular Lie algebras up to dimension 5 which carry LCP structures, and study the existence of lattices in the corresponding simply connected Lie groups.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881692","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}

{"title":"Vertex-primitive digraphs with large fixity","authors":"Marco Barbieri,&nbsp;Primož Potočnik","doi":"10.1007/s10231-024-01447-x","DOIUrl":"10.1007/s10231-024-01447-x","url":null,"abstract":"<div><p>The relative fixity of a digraph <span>(Gamma )</span> is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of <span>(Gamma )</span> and the number of vertices of <span>(Gamma )</span>. We characterize the vertex-primitive digraphs whose relative fixity is at least <span>(frac{1}{3})</span>, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01447-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575731","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}

{"title":"Flow by Gauss curvature to the orlicz chord Minkowski problem","authors":"Xia Zhao,&nbsp;Peibiao Zhao","doi":"10.1007/s10231-024-01448-w","DOIUrl":"10.1007/s10231-024-01448-w","url":null,"abstract":"<div><p>The <span>(L_p)</span> chord Minkowski problem based on chord measures and <span>(L_p)</span> chord measures introduced firstly by Lutwak et al. (Comm Pure Appl Math 1–54, 2023) is a very important and meaningful geometric measure problem in the <span>(L_p)</span> Brunn–Minkowski theory. Xi et al. (Adv Nonlinear Stud 23:20220041, 2023) using variational methods gave a measure solution when <span>(p &gt; 1)</span> and <span>(0&lt;p&lt;1)</span> in the symmetric case. Recently, Guo et al. (Math Ann 2023. 10.1007/s00208-023-02721-8) also obtained a measure solution for <span>(0le p&lt;1)</span> by similar methods without the symmetric assumption. In the present paper, we investigate and confirm the orlicz chord Minkowski problem, which generalizes the <span>(L_p)</span> chord Minkowski problem by replacing <i>p</i> with a fixed continuous function <span>(varphi :(0,infty )rightarrow (0,infty ))</span>, and achieve the existence of smooth solutions to the orlicz chord Minkowski problem by using methods of Gauss curvature flows.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576098","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}

{"title":"Higher integrability for singular doubly nonlinear systems","authors":"Kristian Moring,&nbsp;Leah Schätzler,&nbsp;Christoph Scheven","doi":"10.1007/s10231-024-01443-1","DOIUrl":"10.1007/s10231-024-01443-1","url":null,"abstract":"<div><p>We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is </p><div><div><span>$$begin{aligned} partial _t left( |u|^{q-1}u right) -{{,textrm{div},}}left( |Du|^{p-2} Du right) = {{,textrm{div},}}left( |F|^{p-2} F right) quad text { in } Omega _T:= Omega times (0,T) end{aligned}$$</span></div></div><p>with parameters <span>(p&gt;1)</span> and <span>(q&gt;0)</span> and <span>(Omega subset {mathbb {R}}^n)</span>. In this paper, we are concerned with the ranges <span>(q&gt;1)</span> and <span>(p&gt;frac{n(q+1)}{n+q+1})</span>. A key ingredient in the proof is an intrinsic geometry that takes both the solution <i>u</i> and its spatial gradient <i>Du</i> into account.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01443-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887834","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}

{"title":"Tensor products and intertwining operators between two uniserial representations of the Galilean Lie algebra (mathfrak {sl}(2) < imes {mathfrak {h}}_n)","authors":"Leandro Cagliero,&nbsp;Iván Gómez-Rivera","doi":"10.1007/s10231-024-01439-x","DOIUrl":"10.1007/s10231-024-01439-x","url":null,"abstract":"<div><p>Let <span>(mathfrak {sl}(2) &lt; imes {mathfrak {h}}_n)</span>, <span>(nge 1)</span>, be the Galilean Lie algebra over a field of characteristic zero, here <span>({mathfrak {h}}_{n})</span> is the Heisenberg Lie algebra of dimension <span>(2n+1)</span>, and <span>(mathfrak {sl}(2))</span> acts on <span>({mathfrak {h}}_{n})</span> so that, <span>(mathfrak {sl}(2))</span>-modules, <span>({mathfrak {h}}_nsimeq V(2n-1)oplus V(0))</span> (here <i>V</i>(<i>k</i>) denotes the irreducible <span>(mathfrak {sl}(2))</span>-module of highest weight <i>k</i>). In this paper, we study the tensor product of two uniserial representations of <span>(mathfrak {sl}(2) &lt; imes {mathfrak {h}}_n)</span>. We obtain the <span>(mathfrak {sl}(2))</span>-module structure of the socle of <span>(Votimes W)</span> and we describe the space of intertwining operators <span>(text {Hom}_{mathfrak {sl}(2) &lt; imes {mathfrak {h}}_n}(V,W))</span>, where <i>V</i> and <i>W</i> are uniserial representations of <span>(mathfrak {sl}(2) &lt; imes {mathfrak {h}}_n)</span>. The structure of the radical of <span>(Votimes W)</span> follows from that of the socle of <span>(V^*otimes W^*)</span>. The result is subtle and shows how difficult is to obtain the whole socle series of arbitrary tensor products of uniserials. In contrast to the serial associative case, our results for <span>(mathfrak {sl}(2) &lt; imes {mathfrak {h}}_n)</span> reveal that these tensor products are far from being a direct sum of uniserials; in particular, there are cases in which the tensor product of two uniserial <span>(big (mathfrak {sl}(2) &lt; imes {mathfrak {h}}_nbig ))</span>-modules is indecomposable but not uniserial. Recall that a foundational result of T. Nakayama states that every finitely generated module over a serial associative algebra is a direct sum of uniserial modules. This article extends a previous work in which we obtained the corresponding results for the Lie algebra <span>(mathfrak {sl}(2) &lt; imes {mathfrak {a}}_m)</span> where <span>({mathfrak {a}}_m)</span> is the abelian Lie algebra of dimension <span>(m+1)</span> and <span>(mathfrak {sl}(2))</span> acts so that <span>({mathfrak {a}}_msimeq V(m))</span> as <span>(mathfrak {sl}(2))</span>-modules.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140734984","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}