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Solvability of a class of fully nonlinear elliptic equations on tori tori上一类完全非线性椭圆型方程的可解性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-31 DOI: 10.1007/s10231-023-01342-x
Elia Fusi
{"title":"Solvability of a class of fully nonlinear elliptic equations on tori","authors":"Elia Fusi","doi":"10.1007/s10231-023-01342-x","DOIUrl":"10.1007/s10231-023-01342-x","url":null,"abstract":"<div><p>We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi–Yau type problems in torus bundles.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50529705","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
Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions 具有Dirichlet边界条件的完全非线性退化椭圆障碍系统
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-28 DOI: 10.1007/s10231-023-01343-w
Savvas Andronicou, Emmanouil Milakis
{"title":"Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions","authors":"Savvas Andronicou,&nbsp;Emmanouil Milakis","doi":"10.1007/s10231-023-01343-w","DOIUrl":"10.1007/s10231-023-01343-w","url":null,"abstract":"<div><p>In this paper, we prove existence and uniqueness of viscosity solutions to the following system: For <span>( iin left{ 1,2,dots ,mright} )</span></p><div><div><span>$$begin{aligned}{} &amp; {} min biggl { Fbigl ( y,x,u_{i}(y,x),D u_{i}(y,x),D^2 u_{i}(y,x)bigl ), u_{i}(y,x)-max _{jne i}bigl ( u_{j}(y,x)-c_{ij}(y,x)bigl )biggl }{} &amp; {} =0, left( y,x right) in Omega _{L}{} &amp; {} u_{i}(0,x)=g_{i}(x), xin bar{Omega }, u_i(y,x)=f_i(y,x), (y,x)in (0,L)times partial {Omega } end{aligned}$$</span></div></div><p>where <span>( Omega subset mathbb {R}^n )</span> is a bounded domain, <span>( Omega _{L}:=(0,L)times Omega )</span> and <span>( F:left[ 0,Lright] times mathbb {R}^ntimes mathbb {R}times mathbb {R}^ntimes mathcal {S}^nrightarrow mathbb {R})</span> is a general second-order partial differential operator which covers even the fully nonlinear case. (We will call a second-order partial differential operator <span>(F:left[ 0,Lright] times mathbb {R}^ntimes mathbb {R}times mathbb {R}^ntimes mathcal {S}^nrightarrow mathbb {R})</span> fully nonlinear if and only if, it has the following form </p><div><div><span>$$begin{aligned} F left( y,x,u,D_x u,D_{xx}^2 uright) :=sum _{|alpha |=2}alpha _{alpha }left( y,x,u,D_x u,D_{xx}^2 u right) D^{alpha }u(y,x)+alpha _{0}left( y,x,u,D_x u right) end{aligned}$$</span></div></div><p>with the restriction that at least one of the functional coefficients <span>( alpha _{alpha }, |alpha |=2, )</span> contains a partial derivative term of second order.) Moreover, <i>F</i> belongs to an appropriate subclass of degenerate elliptic operators. Regarding uniqueness, we establish a comparison principle for viscosity sub and supersolutions of the Dirichlet problem. This system appears among others in the theory of the so-called optimal switching problems on bounded domains.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50521569","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 finitely nondegenerate closed homogeneous CR manifolds 关于有限非退化闭齐次CR流形
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-18 DOI: 10.1007/s10231-023-01337-8
Stefano Marini, Costantino Medori, Mauro Nacinovich
{"title":"On finitely nondegenerate closed homogeneous CR manifolds","authors":"Stefano Marini,&nbsp;Costantino Medori,&nbsp;Mauro Nacinovich","doi":"10.1007/s10231-023-01337-8","DOIUrl":"10.1007/s10231-023-01337-8","url":null,"abstract":"<div><p>A complex flag manifold <span>(textsf {F}{=}{{textbf {G}}}/{{textbf {Q}}})</span> decomposes into finitely many real orbits under the action of a real form <span>({{textbf {G}}}^upsigma )</span> of <span>({{textbf {G}}})</span>. Their embedding into <span>(textsf {F})</span> defines on them CR manifold structures. We characterize and list all the closed real orbits which are finitely nondegenerate.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50494600","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 (kappa )-nullity of Riemannian manifolds and their splitting tensors 黎曼流形的零性及其分裂张量
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-18 DOI: 10.1007/s10231-023-01330-1
Claudio Gorodski, Felippe Guimarães
{"title":"The (kappa )-nullity of Riemannian manifolds and their splitting tensors","authors":"Claudio Gorodski,&nbsp;Felippe Guimarães","doi":"10.1007/s10231-023-01330-1","DOIUrl":"10.1007/s10231-023-01330-1","url":null,"abstract":"<div><p>We consider Riemannian <i>n</i>-manifolds <i>M</i> with nontrivial <span>(kappa )</span>-nullity “distribution” of the curvature tensor <i>R</i>, namely, the variable rank distribution of tangent subspaces to <i>M</i> where <i>R</i> coincides with the curvature tensor of a space of constant curvature <span>(kappa )</span> (<span>(kappa in mathbb {R})</span>) is nontrivial. We obtain classification theorems under diferent additional assumptions, in terms of low nullity/conullity, controlled scalar curvature or existence of quotients of finite volume. We prove new results, but also revisit previous ones.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50494446","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
Investigating rational perfect nonlinear functions 有理完全非线性函数的研究
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-02 DOI: 10.1007/s10231-023-01339-6
Daniele Bartoli, Marco Timpanella
{"title":"Investigating rational perfect nonlinear functions","authors":"Daniele Bartoli,&nbsp;Marco Timpanella","doi":"10.1007/s10231-023-01339-6","DOIUrl":"10.1007/s10231-023-01339-6","url":null,"abstract":"<div><p>Perfect nonlinear (PN) functions over a finite field, whose study is also motivated by practical applications to Cryptography, have been the subject of several recent papers where the main problems, such as effective constructions and non-existence results, are considered. So far, all contributions have focused on PN functions represented by polynomials, and their constructions. Unfortunately, for polynomial PN functions, the approach based on Hasse–Weil type bounds applied to function fields can only provide non-existence results in a small degree regime. In this paper, we investigate the non-existence problem of rational perfect nonlinear functions over a finite field. Our approach makes it possible to use deep results about the number of points of algebraic varieties over finite fields. Our main result is that no PN rational function <i>f</i>/<i>g</i> with <span>(f,gin mathbb {F}_q[X])</span> exists when certain mild arithmetical conditions involving the degree of <i>f</i>(<i>X</i>) and <i>g</i>(<i>X</i>) are satisfied.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01339-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50441391","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
Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds 紧几乎Kähler流形上的Bott–Chern调和形式和基分解
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-05-02 DOI: 10.1007/s10231-023-01338-7
Riccardo Piovani, Nicoletta Tardini
{"title":"Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds","authors":"Riccardo Piovani,&nbsp;Nicoletta Tardini","doi":"10.1007/s10231-023-01338-7","DOIUrl":"10.1007/s10231-023-01338-7","url":null,"abstract":"<div><p>Let <span>((X,J,omega ))</span> be a compact 2<i>n</i>-dimensional almost Kähler manifold. We prove primitive decompositions for Bott–Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott–Chern, Aeppli, Dolbeault and <span>(partial )</span>-harmonic forms on <span>((X,J,omega ))</span> are related.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01338-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50441390","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: 6
Generalized m-Quasi-Einstein manifolds admitting a closed conformal vector field 允许闭共形向量场的广义m-拟Einstein流形
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-26 DOI: 10.1007/s10231-023-01335-w
Rahul Poddar, S. Balasubramanian, Ramesh Sharma
{"title":"Generalized m-Quasi-Einstein manifolds admitting a closed conformal vector field","authors":"Rahul Poddar,&nbsp;S. Balasubramanian,&nbsp;Ramesh Sharma","doi":"10.1007/s10231-023-01335-w","DOIUrl":"10.1007/s10231-023-01335-w","url":null,"abstract":"<div><p>We study a complete connected generalized <i>m</i>-quasi-Einstein manifold <i>M</i> with finite <i>m</i>, admitting a non-homothetic, non-parallel, complete closed conformal vector field <i>V</i>, and show that either <i>M</i> is isometric to a round sphere, or the Ricci tensor can be expressed explicitly in terms of the conformal data over an open dense subset. In the latter case, we prove that <i>M</i> is a warped product of an open real interval with an Einstein manifold; furthermore, it is conformally flat in dimension 4 and has vanishing Cotton and Bach tensors in dimension &gt; 3. Next, we obtain the same explicit expression for the Ricci tensor, and analogous results, for a gradient Ricci almost soliton endowed with a non-parallel closed conformal vector field.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514895","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 recognition of direct powers of finite simple linear groups by spectrum 有限简单线性群直幂的谱识别
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-26 DOI: 10.1007/s10231-023-01336-9
Nanying Yang, Ilya Gorshkov, Alexey Staroletov, Andrey V. Vasil’ev
{"title":"On recognition of direct powers of finite simple linear groups by spectrum","authors":"Nanying Yang,&nbsp;Ilya Gorshkov,&nbsp;Alexey Staroletov,&nbsp;Andrey V. Vasil’ev","doi":"10.1007/s10231-023-01336-9","DOIUrl":"10.1007/s10231-023-01336-9","url":null,"abstract":"<div><p>The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the <i>Kourovka Notebook</i> proving that for every positive integer <i>k</i>, the <i>k</i>-th direct power of the simple linear group <span>(L_{n}(2))</span> is uniquely determined by its spectrum in the class of finite groups provided <i>n</i> is a power of 2 greater than or equal to <span>(56k^2)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514837","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: 1
Asymptotics of non-local perimeters 非局部周长的渐近性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-24 DOI: 10.1007/s10231-023-01332-z
Wojciech Cygan, Tomasz Grzywny
{"title":"Asymptotics of non-local perimeters","authors":"Wojciech Cygan,&nbsp;Tomasz Grzywny","doi":"10.1007/s10231-023-01332-z","DOIUrl":"10.1007/s10231-023-01332-z","url":null,"abstract":"<div><p>We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on <span>({mathbb {R}}^d)</span> which integrates the function <span>(1wedge |x|)</span>. Such definition of non-local perimeter encompasses a wide range of perimeters which have been already studied in the literature, including fractional perimeters and anisotropic fractional perimeters. The main part of the article is devoted to the study of the asymptotic behaviour of non-local perimeters. As direct applications we recover well-known convergence results for fractional perimeters and anisotropic fractional perimeters.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01332-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509362","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
Microlocal analysis for Gelfand–Shilov spaces Gelfand–Shilov空间的微观局部分析
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-21 DOI: 10.1007/s10231-023-01324-z
Luigi Rodino, Patrik Wahlberg
{"title":"Microlocal analysis for Gelfand–Shilov spaces","authors":"Luigi Rodino,&nbsp;Patrik Wahlberg","doi":"10.1007/s10231-023-01324-z","DOIUrl":"10.1007/s10231-023-01324-z","url":null,"abstract":"<div><p>We introduce an anisotropic global wave front set of Gelfand–Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the lack of super-exponential decay along power type curves in the phase space of the short-time Fourier transform. This wave front set captures the phase space behaviour of oscillations of power monomial type, a k a chirp signals. A microlocal result is proved with respect to pseudodifferential operators with symbol classes that give rise to continuous operators on Gelfand–Shilov spaces. We determine the wave front set of certain series of derivatives of the Dirac delta, and exponential functions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01324-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500584","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
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