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Algebra and geometry of Sobolev embeddings Sobolev嵌入的代数和几何
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-04-03 DOI: 10.4171/rlm/889
A. Visintin
{"title":"Algebra and geometry of Sobolev embeddings","authors":"A. Visintin","doi":"10.4171/rlm/889","DOIUrl":"https://doi.org/10.4171/rlm/889","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":"28 1","pages":"249-267"},"PeriodicalIF":0.5,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83545092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Totally $T$-adic functions of small height 总$T$-小高度的adic函数
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-03-11 DOI: 10.4171/RLM/911
X. Faber, Clayton Petsche
{"title":"Totally $T$-adic functions of small height","authors":"X. Faber, Clayton Petsche","doi":"10.4171/RLM/911","DOIUrl":"https://doi.org/10.4171/RLM/911","url":null,"abstract":"Let $mathbb{F}_q(T)$ be the field of rational functions in one variable over a finite field. We introduce the notion of a totally $T$-adic function: one that is algebraic over $mathbb{F}_q(T)$ and whose minimal polynomial splits completely over the completion $mathbb{F}_q(!(T)!)$. We give two proofs that the height of a nonconstant totally $T$-adic function is bounded away from zero, each of which provides a sharp lower bound. We spend the majority of the paper providing explicit constructions of totally $T$-adic functions of small height (via arithmetic dynamics) and minimum height (via geometry and computer search). We also execute a large computer search that proves certain kinds of totally $T$-adic functions of minimum height over $mathbb{F}_2(T)$ do not exist. The problem of whether there exist infinitely many totally $T$-adic functions of minimum positive height over $mathbb{F}_q(T)$ remains open. Finally, we consider analogues of these notions under additional integrality hypotheses.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49642886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Duality and distance formulas in Lipschitz–Hölder spaces Lipschitz-Hölder空间中的对偶性和距离公式
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-12-11 DOI: 10.4171/rlm/897
Francesca Angrisani, G. Ascione, Luigi d’Onofrio, Gianluigi Manzo
{"title":"Duality and distance formulas in Lipschitz–Hölder spaces","authors":"Francesca Angrisani, G. Ascione, Luigi d’Onofrio, Gianluigi Manzo","doi":"10.4171/rlm/897","DOIUrl":"https://doi.org/10.4171/rlm/897","url":null,"abstract":"For a compact metric space $(K, rho)$, the predual of $Lip(K, rho)$ can be identified with the normed space $M(K)$ of finite (signed) Borel measures on $K$ equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of $M(K)$ by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between $Lip(K, rho)$ and $(lip(K, rho))_{**}$ [15]. In this work we also show that the pair $(lip(K, rho), Lip(K, rho))$ can be framed in the theory of o-O type structures introduced by K. M. Perfekt.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/897","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48757407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 8
Hopf bifurcations and global nonlinear $L^2$-energy stability in thermal MHD 热MHD的Hopf分岔和全局非线性L^2 -能量稳定性
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-11-05 DOI: 10.4171/rlm/874
S. Rionero
{"title":"Hopf bifurcations and global nonlinear $L^2$-energy stability in thermal MHD","authors":"S. Rionero","doi":"10.4171/rlm/874","DOIUrl":"https://doi.org/10.4171/rlm/874","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42549498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 8
The Dirichlet problem with VMO data in upper-graph Lipschitz domains 上图Lipschitz域中VMO数据的Dirichlet问题
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-11-05 DOI: 10.4171/rlm/868
D. Mitrea, I. Mitrea, M. Mitrea
{"title":"The Dirichlet problem with VMO data in upper-graph Lipschitz domains","authors":"D. Mitrea, I. Mitrea, M. Mitrea","doi":"10.4171/rlm/868","DOIUrl":"https://doi.org/10.4171/rlm/868","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/868","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45245518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Eight(y) mathematical questions on fluids and structures 关于流体和结构的八个数学问题
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-11-01 DOI: 10.4171/rlm/870
D. Bonheure, F. Gazzola, G. Sperone
{"title":"Eight(y) mathematical questions on fluids and structures","authors":"D. Bonheure, F. Gazzola, G. Sperone","doi":"10.4171/rlm/870","DOIUrl":"https://doi.org/10.4171/rlm/870","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/870","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46709574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 10
Homogenization of the backward-forward meanfield games systems in periodic environments 周期环境下后向平均场博弈系统的均匀化
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-09-03 DOI: 10.4171/RLM/912
P. Lions, P. Souganidis
{"title":"Homogenization of the backward-forward meanfield games systems in periodic environments","authors":"P. Lions, P. Souganidis","doi":"10.4171/RLM/912","DOIUrl":"https://doi.org/10.4171/RLM/912","url":null,"abstract":"We study the homogenization properties in the small viscosity limit and in periodic environments of the (viscous) backward-forward mean-field games system. We consider separated Hamiltonians and provide results for systems with (i) \"smoothing\" coupling and general initial and terminal data, and (ii) with \"local coupling\" but well-prepared data.The limit is a first-order forward-backward system. In the nonlocal coupling case, the averaged system is of mfg-type, which is well-posed in some cases. For the problems with local coupling, the homogenization result is proved assuming that the formally obtained limit system has smooth solutions with well prepared initial and terminal data. It is also shown, using a very general example (potential mfg), that the limit system is not necessarily of mfg-type.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44092113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Linear functionals on variable exponent Bochner–Lebesgue spaces 变指数Bochner–Lebesgue空间上的线性泛函
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-09-02 DOI: 10.4171/rlm/861
R. E. Castillo, O. Guzmán, H. Rafeiro
{"title":"Linear functionals on variable exponent Bochner–Lebesgue spaces","authors":"R. E. Castillo, O. Guzmán, H. Rafeiro","doi":"10.4171/rlm/861","DOIUrl":"https://doi.org/10.4171/rlm/861","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/861","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45720359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Density in SBD and approximation of fracture energies SBD中的密度与断裂能的近似
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-09-02 DOI: 10.4171/rlm/859
V. Crismale
{"title":"Density in SBD and approximation of fracture energies","authors":"V. Crismale","doi":"10.4171/rlm/859","DOIUrl":"https://doi.org/10.4171/rlm/859","url":null,"abstract":". We prove three density theorems, in the strong BD topology, for the three subspaces of SBD functions: SBD ; SBD p ∞ , where the absolutely continuous part of the symmetric gradient is in L p , with p > 1 ; SBD p , whose functions are in SBD p ∞ and the jump set has fi-nite H n − 1 -measure. We compare them with existing results, discussing related approximation of fracture energies.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44511619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
On a new necessary condition in the Calculus of Variations for Lagrangians that are highly discontinuous in the state and velocity 状态和速度高度不连续的拉格朗日量在变分学中的一个新的必要条件
IF 0.5 4区 数学
Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-09-02 DOI: 10.4171/rlm/865
P. Bettiol, C. Mariconda
{"title":"On a new necessary condition in the Calculus of Variations for Lagrangians that are highly discontinuous in the state and velocity","authors":"P. Bettiol, C. Mariconda","doi":"10.4171/rlm/865","DOIUrl":"https://doi.org/10.4171/rlm/865","url":null,"abstract":"","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/865","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42158995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
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