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Annali di Matematica Pura ed Applicata最新文献

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Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator 域上Besov型和Triebel-Lizorkin型空间的极限嵌入和一个扩展算子
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-27 DOI: 10.1007/s10231-023-01327-w
Helena F. Gonçalves, Dorothee D. Haroske, Leszek Skrzypczak
{"title":"Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator","authors":"Helena F. Gonçalves,&nbsp;Dorothee D. Haroske,&nbsp;Leszek Skrzypczak","doi":"10.1007/s10231-023-01327-w","DOIUrl":"10.1007/s10231-023-01327-w","url":null,"abstract":"<div><p>In this paper, we study limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces, <span>(text {id}_tau : {B}_{p_1,q_1}^{s_1,tau _1}(Omega ) hookrightarrow {B}_{p_2,q_2}^{s_2,tau _2}(Omega ))</span> and <span>(text {id}_tau : {F}_{p_1,q_1}^{s_1,tau _1}(Omega ) hookrightarrow {F}_{p_2,q_2}^{s_2,tau _2}(Omega ))</span>, where <span>(Omega subset {{{mathbb {R}}}^d})</span> is a bounded domain, obtaining necessary and sufficient conditions for the continuity of <span>(text {id}_tau )</span>. This can also be seen as the continuation of our previous studies of compactness of the embeddings in the non-limiting case. Moreover, we also construct Rychkov’s linear, bounded universal extension operator for these spaces.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01327-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50518417","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: 2
A singular Liouville equation on two-dimensional domains 二维域上的奇异Liouville方程
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-24 DOI: 10.1007/s10231-023-01326-x
Marcelo Montenegro, Matheus F. Stapenhorst
{"title":"A singular Liouville equation on two-dimensional domains","authors":"Marcelo Montenegro,&nbsp;Matheus F. Stapenhorst","doi":"10.1007/s10231-023-01326-x","DOIUrl":"10.1007/s10231-023-01326-x","url":null,"abstract":"<div><p>We prove the existence of a solution for an equation where the nonlinearity is singular at zero, namely <span>(-Delta u =(-u^{-beta }+f(u))chi _{{u&gt;0}})</span> in <span>(Omega subset {mathbb {R}}^{2})</span> with Dirichlet boundary condition. The function <i>f</i> grows exponentially, which can be subcritical or critical with respect to the Trudinger–Moser embedding. We examine the functional <span>(I_epsilon )</span> corresponding to the <span>(epsilon )</span>-perturbed equation <span>(-Delta u + g_epsilon (u) = f(u))</span>, where <span>(g_epsilon )</span> tends pointwisely to <span>(u^{-beta })</span> as <span>(epsilon rightarrow 0^+)</span>. We show that <span>(I_epsilon )</span> possesses a critical point <span>(u_epsilon )</span> in <span>(H_0^1(Omega ))</span>, which converges to a genuine nontrivial nonnegative solution of the original problem as <span>(epsilon rightarrow 0)</span>. We also address the problem with <i>f</i>(<i>u</i>) replaced by <span>(lambda f(u))</span>, when the parameter <span>(lambda &gt;0)</span> is sufficiently large. We give examples.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01326-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50510610","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 representation formula for slice regular functions over slice-cones in several variables 多变量切片锥上切片正则函数的一个表示公式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-24 DOI: 10.1007/s10231-023-01325-y
Xinyuan Dou, Guangbin Ren, Irene Sabadini
{"title":"A representation formula for slice regular functions over slice-cones in several variables","authors":"Xinyuan Dou,&nbsp;Guangbin Ren,&nbsp;Irene Sabadini","doi":"10.1007/s10231-023-01325-y","DOIUrl":"10.1007/s10231-023-01325-y","url":null,"abstract":"<div><p>The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form <span>({mathbb {R}}^{2n})</span>. This is a new setting which contains and encompasses in a nontrivial way other cases already studied in the literature and which requires new tools. To this end, we define a cone <span>({mathcal {W}}_{mathcal {C}}^d)</span> in <span>([{text {End}}({mathbb {R}}^{2n})]^d)</span> and we extend the slice topology <span>(tau _s)</span> to this cone. Slice regular functions can be defined on open sets in <span>(left( tau _s,{mathcal {W}}_{mathcal {C}}^dright) )</span> and a number of results can be proved in this framework, among which a representation formula. This theory can be applied to some real algebras, called left slice complex structure algebras. These algebras include quaternions, octonions, Clifford algebras and real alternative <span>(*)</span>-algebras but also left-alternative algebras and sedenions, thus providing brand new settings in slice analysis.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01325-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50511299","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: 3
Canonical Witt formal scheme extensions and p-torsion groups 正则Witt形式方案的扩展与p-托离子群
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-23 DOI: 10.1007/s10231-023-01321-2
Alessandra Bertapelle, Nicola Mazzari, Arnab Saha
{"title":"Canonical Witt formal scheme extensions and p-torsion groups","authors":"Alessandra Bertapelle,&nbsp;Nicola Mazzari,&nbsp;Arnab Saha","doi":"10.1007/s10231-023-01321-2","DOIUrl":"10.1007/s10231-023-01321-2","url":null,"abstract":"<div><p>We study the <b><i>n</i></b>th arithmetic jet space of the <b><i>p</i></b>-torsion subgroup attached to a smooth commutative formal group scheme. We show that the <b><i>n</i></b>th jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length <b><i>n</i></b> and the <b><i>p</i></b>-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01321-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50508360","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 boundary complex of the k-Cauchy–Fueter complex 关于k-Cauchy-Fueter复形的边界复形
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-16 DOI: 10.1007/s10231-023-01319-w
Wei Wang
{"title":"On the boundary complex of the k-Cauchy–Fueter complex","authors":"Wei Wang","doi":"10.1007/s10231-023-01319-w","DOIUrl":"10.1007/s10231-023-01319-w","url":null,"abstract":"<div><p>The <i>k</i>-Cauchy–Fueter complex, <span>(k=0,1,ldots )</span>, in quaternionic analysis are the counterpart of the Dolbeault complex in the theory of several complex variables. In this paper, we construct explicitly boundary complexes of these complexes on boundaries of domains, corresponding to the tangential Cauchy–Riemann complex in complex analysis. They are only known boundary complexes outside of complex analysis that have interesting applications to the function theory. As an application, we establish the Hartogs–Bochner extension for <i>k</i>-regular functions, the quaternionic counterpart of holomorphic functions. These boundary complexes have a very simple form on a kind of quadratic hypersurfaces, which have the structure of right-type nilpotent Lie groups of step two. They allow us to introduce the quaternionic Monge–Ampère operator and open the door to investigate pluripotential theory on such groups. We also apply abstract duality theorem to boundary complexes to obtain the generalization of Malgrange’s vanishing theorem and the Hartogs–Bochner extension for <i>k</i>-CF functions, the quaternionic counterpart of CR functions, on this kind of groups.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01319-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50488008","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: 1
An inhomogeneous version of the Carleson estimate for singular/degenerate nonlinear equations 奇异/退化非线性方程Carleson估计的非齐次形式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-16 DOI: 10.1007/s10231-023-01320-3
J. Ederson M. Braga, Diego R. Moreira, J. Wálisson V. de Sousa
{"title":"An inhomogeneous version of the Carleson estimate for singular/degenerate nonlinear equations","authors":"J. Ederson M. Braga,&nbsp;Diego R. Moreira,&nbsp;J. Wálisson V. de Sousa","doi":"10.1007/s10231-023-01320-3","DOIUrl":"10.1007/s10231-023-01320-3","url":null,"abstract":"<div><p>In this paper, we provide an inhomogeneous version of the Carleson estimate for quasilinear elliptic equations with g-Laplace type growth and unbounded right-hand side. We use this result to extend exponential growth theorems in cylindrical unbounded domains proven by Berestycki et al. (Duke Math J 81:467–494, 1996). We finish this paper showing a boundary Harnack-type inequality.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01320-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50487607","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
Yamabe solitons with boundary 带边界的Yamabe孤子
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-09 DOI: 10.1007/s10231-023-01318-x
Pak Tung Ho, Jinwoo Shin
{"title":"Yamabe solitons with boundary","authors":"Pak Tung Ho,&nbsp;Jinwoo Shin","doi":"10.1007/s10231-023-01318-x","DOIUrl":"10.1007/s10231-023-01318-x","url":null,"abstract":"<div><p>Yamabe soliton is a self-similar solution to the Yamabe flow on manifolds without boundary. In this paper, we define and study the Yamabe soliton with boundary and conformal mean curvature soliton, which are natural generalizations of the Yamabe soliton. We study these solitons from equation point of view. We also study their two-dimensional analog: the Gauss curvature soliton with boundary and geodesic curvature soliton.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01318-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50466457","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 a Nirenberg-type problem involving the half Laplacian: density and multiplicity of solutions 关于半拉普拉斯算子的Nirenberg型问题：解的密度和多重性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-06 DOI: 10.1007/s10231-023-01316-z
Zhongwei Tang, Heming Wang, Ning Zhou
{"title":"On a Nirenberg-type problem involving the half Laplacian: density and multiplicity of solutions","authors":"Zhongwei Tang,&nbsp;Heming Wang,&nbsp;Ning Zhou","doi":"10.1007/s10231-023-01316-z","DOIUrl":"10.1007/s10231-023-01316-z","url":null,"abstract":"<div><p>In this paper, we study a Nirenberg-type problem involving the half Laplacian. By applying the minimax procedure introduced by Coti Zelati and Rabinowitz and combining the blow-up analysis arguments, we obtain a <span>(C^0)</span> density result and also the existence of infinitely many multi-bump solutions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50456993","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: 2
Geometry of tree-based tensor formats in tensor Banach spaces 张量Banach空间中基于树的张量格式的几何
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-04 DOI: 10.1007/s10231-023-01315-0
Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy
{"title":"Geometry of tree-based tensor formats in tensor Banach spaces","authors":"Antonio Falcó,&nbsp;Wolfgang Hackbusch,&nbsp;Anthony Nouy","doi":"10.1007/s10231-023-01315-0","DOIUrl":"10.1007/s10231-023-01315-0","url":null,"abstract":"<div><p>In the paper <i>‘On the Dirac–Frenkel Variational Principle on Tensor Banach Spaces’</i>, we provided a geometrical description of manifolds of tensors in Tucker format with fixed multilinear (or Tucker) rank in tensor Banach spaces, that allowed to extend the Dirac–Frenkel variational principle in the framework of topological tensor spaces. The purpose of this note is to extend these results to more general tensor formats. More precisely, we provide a new geometrical description of manifolds of tensors in tree-based (or hierarchical) format, also known as tree tensor networks, which are intersections of manifolds of tensors in Tucker format associated with different partitions of the set of dimensions. The proposed geometrical description of tensors in tree-based format is compatible with the one of manifolds of tensors in Tucker format.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01315-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50449903","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: 5
Curvature properties of 3-((alpha ,delta ))-Sasaki manifolds 3-（（alpha，delta）-Sasaki流形的曲率性质
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-03 DOI: 10.1007/s10231-023-01310-5
Ilka Agricola, Giulia Dileo, Leander Stecker
{"title":"Curvature properties of 3-((alpha ,delta ))-Sasaki manifolds","authors":"Ilka Agricola,&nbsp;Giulia Dileo,&nbsp;Leander Stecker","doi":"10.1007/s10231-023-01310-5","DOIUrl":"10.1007/s10231-023-01310-5","url":null,"abstract":"<div><p>We investigate curvature properties of 3-<span>((alpha ,delta ))</span>-Sasaki manifolds, a special class of almost 3-contact metric manifolds generalizing 3-Sasaki manifolds (corresponding to <span>(alpha =delta =1)</span>) that admit a canonical metric connection with skew torsion and define a Riemannian submersion over a quaternionic Kähler manifold with vanishing, positive or negative scalar curvature, according to <span>(delta =0)</span>, <span>(alpha delta &gt;0)</span> or <span>(alpha delta &lt;0)</span>. We shall investigate both the Riemannian curvature and the curvature of the canonical connection, with particular focus on their curvature operators, regarded as symmetric endomorphisms of the space of 2-forms. We describe their spectrum, find distinguished eigenforms, and study the conditions of strongly definite curvature in the sense of Thorpe.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01310-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50446475","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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