Pub Date : 2023-04-13DOI: 10.2422/2036-2145.202112_009
Takashi Kagaya, M. Mizuno, K. Takasao
{"title":"Long time behavior for a curvature flow of networks related to grain boundary motion with the effect of lattice misoriantations","authors":"Takashi Kagaya, M. Mizuno, K. Takasao","doi":"10.2422/2036-2145.202112_009","DOIUrl":"https://doi.org/10.2422/2036-2145.202112_009","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"436 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76667503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.2422/2036-2145.202208_006
Chaoqiang Tan, Yanchang Han, Yongsheng Han, Ming-Yi Lee, Ji Li
{"title":"Criterion of the L2 boundedness in Dunkl setting and applications","authors":"Chaoqiang Tan, Yanchang Han, Yongsheng Han, Ming-Yi Lee, Ji Li","doi":"10.2422/2036-2145.202208_006","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_006","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81717716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.2422/2036-2145.202208_019
Bogdan–Vasile Matioc, Christoph Walker
{"title":"The Nonlocal Mean Curvature Flow of Periodic Graphs","authors":"Bogdan–Vasile Matioc, Christoph Walker","doi":"10.2422/2036-2145.202208_019","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_019","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78991711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-20DOI: 10.2422/2036-2145.202106_020
L. Palmisano
{"title":"Laminations of Coexisting Attractors","authors":"L. Palmisano","doi":"10.2422/2036-2145.202106_020","DOIUrl":"https://doi.org/10.2422/2036-2145.202106_020","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"122 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87644250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-20DOI: 10.2422/2036-2145.202109_011
H. Kozono, Peer Christian Kunstmann, Senjo Shimizu
{"title":"Analyticity in space-time of solutions to the Navier-Stokes equations via parameter trick based on maximal regularity","authors":"H. Kozono, Peer Christian Kunstmann, Senjo Shimizu","doi":"10.2422/2036-2145.202109_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202109_011","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"89 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90875413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-06DOI: 10.2422/2036-2145.202301_004
Mi Hu
In this paper, we investigate the behavior of orbits inside attracting basins in higher dimensions. Suppose $F(z, w)=(P(z), Q(w))$, where $P(z), Q(w)$ are two polynomials of degree $m_1, m_2geq2$ on $mathbb{C}$, $P(0)=Q(0)=0,$ and $0<|P'(0)|, |Q'(0)|<1.$ Let $Omega$ be the immediate attracting basin of $F(z, w)$. Then there is a constant $C$ such that for every point $(z_0, w_0)in Omega$, there exists a point $(tilde{z}, tilde{w})in cup_k F^{-k}(0, 0), kgeq0$ so that $d_Omegabig((z_0, w_0), (tilde{z}, tilde{w})big)leq C, d_Omega$ is the Kobayashi distance on $Omega$. However, for many other cases, this result is invalid.
{"title":"Dynamics inside Fatou sets in higher dimensions","authors":"Mi Hu","doi":"10.2422/2036-2145.202301_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202301_004","url":null,"abstract":"In this paper, we investigate the behavior of orbits inside attracting basins in higher dimensions. Suppose $F(z, w)=(P(z), Q(w))$, where $P(z), Q(w)$ are two polynomials of degree $m_1, m_2geq2$ on $mathbb{C}$, $P(0)=Q(0)=0,$ and $0<|P'(0)|, |Q'(0)|<1.$ Let $Omega$ be the immediate attracting basin of $F(z, w)$. Then there is a constant $C$ such that for every point $(z_0, w_0)in Omega$, there exists a point $(tilde{z}, tilde{w})in cup_k F^{-k}(0, 0), kgeq0$ so that $d_Omegabig((z_0, w_0), (tilde{z}, tilde{w})big)leq C, d_Omega$ is the Kobayashi distance on $Omega$. However, for many other cases, this result is invalid.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81587938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-27DOI: 10.2422/2036-2145.202208_011
N. Karpenko
{"title":"Chow ring of BSO(2n) in characteristic 2","authors":"N. Karpenko","doi":"10.2422/2036-2145.202208_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_011","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"307 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77944369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-17DOI: 10.2422/2036-2145.202203_003
G. Curbera, S. Okada, W. Ricker
. The finite Hilbert transform T is a singular integral operator which maps the Zygmund space L log L := L log L ( − 1 , 1) continuously into L 1 := L 1 ( − 1 , 1). By extending the Parseval and Poincar´e-Bertrand formulae to this setting, it is possible to establish an inversion result needed for solving the airfoil equation T ( f ) = g whenever the data function g lies in the range of T within L 1 (shown to contain L (log L ) 2 ). Until now this was only known for g belonging to the union of all L p spaces with p > 1. It is established (due to a result of Stein) that T cannot be extended to any domain space beyond L log L whilst still taking its values in L 1 , i.e., T : L log L → L 1 is optimally defined.
{"title":"The finite Hilbert transform acting in the Zygmund space LlogL","authors":"G. Curbera, S. Okada, W. Ricker","doi":"10.2422/2036-2145.202203_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202203_003","url":null,"abstract":". The finite Hilbert transform T is a singular integral operator which maps the Zygmund space L log L := L log L ( − 1 , 1) continuously into L 1 := L 1 ( − 1 , 1). By extending the Parseval and Poincar´e-Bertrand formulae to this setting, it is possible to establish an inversion result needed for solving the airfoil equation T ( f ) = g whenever the data function g lies in the range of T within L 1 (shown to contain L (log L ) 2 ). Until now this was only known for g belonging to the union of all L p spaces with p > 1. It is established (due to a result of Stein) that T cannot be extended to any domain space beyond L log L whilst still taking its values in L 1 , i.e., T : L log L → L 1 is optimally defined.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86086067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-15DOI: 10.2422/2036-2145.202302_004
Lukas Niebel, Rico Zacher
In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which combines an $L^p-L^infty$-estimate with a weak $L^1$-estimate for the logarithm of supersolutions. In this note, we give a novel proof of this weak $L^1$-estimate. The presented argument uses parabolic trajectories and does not use any Poincar'e inequality. Moreover, the proposed argument gives a geometric interpretation of Moser's result and could allow transferring Moser's method to other equations.
{"title":"A trajectorial interpretation of Moser’s proof of the Harnack inequality","authors":"Lukas Niebel, Rico Zacher","doi":"10.2422/2036-2145.202302_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202302_004","url":null,"abstract":"In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which combines an $L^p-L^infty$-estimate with a weak $L^1$-estimate for the logarithm of supersolutions. In this note, we give a novel proof of this weak $L^1$-estimate. The presented argument uses parabolic trajectories and does not use any Poincar'e inequality. Moreover, the proposed argument gives a geometric interpretation of Moser's result and could allow transferring Moser's method to other equations.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"194 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79746206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-13DOI: 10.2422/2036-2145.202206_005
A. Fernandes, J. E. Sampaio
We classify semi-algebraic surfaces in $mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.
{"title":"Global bi-Lipschitz classification of semialgebraic surfaces","authors":"A. Fernandes, J. E. Sampaio","doi":"10.2422/2036-2145.202206_005","DOIUrl":"https://doi.org/10.2422/2036-2145.202206_005","url":null,"abstract":"We classify semi-algebraic surfaces in $mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"107 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81472292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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