Annali di Matematica Pura ed Applicata最新文献

{"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":"203 5","pages":"2235 - 2274"},"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":"203 5","pages":"2125 - 2155"},"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}

{"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":"203 5","pages":"2319 - 2356"},"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}

{"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":"203 5","pages":"2357 - 2382"},"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}

{"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":"203 5","pages":"2185 - 2198"},"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}

{"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":"203 5","pages":"2199 - 2234"},"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}

{"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":"203 5","pages":"2157 - 2184"},"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}

{"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":"203 5","pages":"2111 - 2124"},"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}

{"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":"203 5","pages":"2057 - 2074"},"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}

{"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":"203 5","pages":"2095 - 2109"},"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}