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Optimal singularities of initial functions for solvability of a semilinear parabolic system 一类半线性抛物型系统可解性的初始函数的最优奇异性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-12-10 DOI: 10.2969/jmsj/86058605
Y. Fujishima, Kazuhiro Ishige
{"title":"Optimal singularities of initial functions for solvability of a semilinear parabolic system","authors":"Y. Fujishima, Kazuhiro Ishige","doi":"10.2969/jmsj/86058605","DOIUrl":"https://doi.org/10.2969/jmsj/86058605","url":null,"abstract":"Let $(u,v)$ be a nonnegative solution to the semilinear parabolic system [ mbox{(P)} qquad cases{ partial_t u=D_1Delta u+v^p, & $xin{bf R}^N,,,,t>0,$ partial_t v=D_2Delta v+u^q, & $xin{bf R}^N,,,,t>0,$ (u(cdot,0),v(cdot,0))=(mu,nu), & $xin{bf R}^N,$ } ] where $D_1$, $D_2>0$, $0 1$ and $(mu,nu)$ is a pair of nonnegative Radon measures or nonnegative measurable functions in ${bf R}^N$. In this paper we study sufficient conditions on the initial data for the solvability of problem~(P) and clarify optimal singularities of the initial functions for the solvability.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48612805","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: 4
Default functions and Liouville type theorems based on symmetric diffusions 基于对称扩散的默认函数和Liouville型定理
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-12-01 DOI: 10.2969/jmsj/82398239
A. Atsuji
{"title":"Default functions and Liouville type theorems based on symmetric diffusions","authors":"A. Atsuji","doi":"10.2969/jmsj/82398239","DOIUrl":"https://doi.org/10.2969/jmsj/82398239","url":null,"abstract":"Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps. Default functions were introduced in [7] and it is known that vanishing of the default function of a local martingale implies that it is a true martingale. Positivity of the default function then indicates the singularity of local martingale. Such local martingales are called strictly local martingales. Recently strictly local martingales are playing important roles in the theory of financial bubbles (cf. [19]), so the notion of default function becomes important in mathematical finance area. We consider them in a different context. In mathematical analysis of subharmonic functions it is classical and natural to consider the functions along Brownian motions. A stochastic process derived from a subharmonic function composed with Brownian motion is a local submartingale. Then if we know that the process is a true submartingale, which follows from vanishing of the default function of the submartingale, it effects simpleness and clearness in analysis of subharmonic functions. In this paper we intend to show that this probabilistic notion plays effective roles in some analysis such as L-Liouville type theorems of subharmonic functions and Liouville type theorems for functions satisfying some nonlinear differential inequalities. It covers and extends the precedent results about L-Liouville theorem for subharmonic functions 2000 Mathematics Subject Classification. Primary 31C05; Secondary 58J65.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43576089","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
Effective Łojasiewicz gradient inequality for Nash functions with application to finite determinacy of germs 有效的Łojasiewicz梯度不等式纳什函数及其在细菌有限确定性中的应用
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-12-01 DOI: 10.2969/jmsj/83378337
Beata Osińska-Ulrych, Grzegorz Skalski, S. Spodzieja
{"title":"Effective Łojasiewicz gradient inequality for Nash functions with application to finite determinacy of germs","authors":"Beata Osińska-Ulrych, Grzegorz Skalski, S. Spodzieja","doi":"10.2969/jmsj/83378337","DOIUrl":"https://doi.org/10.2969/jmsj/83378337","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41454374","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
Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $varepsilon$-range 具有$varepsilon$范围的较低$N$加权Ricci曲率边界下具有边界的流形的几何比较
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-11-07 DOI: 10.2969/jmsj/87278727
K. Kuwae, Y. Sakurai
{"title":"Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $varepsilon$-range","authors":"K. Kuwae, Y. Sakurai","doi":"10.2969/jmsj/87278727","DOIUrl":"https://doi.org/10.2969/jmsj/87278727","url":null,"abstract":"We study comparison geometry of manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $Nin ]-infty,1]cup [n,+infty]$ with $varepsilon$-range introduced by Lu-Minguzzi-Ohta. We will conclude splitting theorems, and also comparison geometric results for inscribed radius, volume around the boundary, and smallest Dirichlet eigenvalue of the weighted $p$-Laplacian. Our results interpolate those for $Nin [n,+infty[$ and $varepsilon=1$, and for $Nin ]-infty,1]$ and $varepsilon=0$ by the second named author.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41582718","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
A mass transportation proof of the sharp one-dimensional Gagliardo–Nirenberg inequalities 一维加利亚多-尼伦堡不等式的大规模运输证明
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-11-01 DOI: 10.2969/jmsj/82258225
V. H. Nguyen
{"title":"A mass transportation proof of the sharp one-dimensional Gagliardo–Nirenberg inequalities","authors":"V. H. Nguyen","doi":"10.2969/jmsj/82258225","DOIUrl":"https://doi.org/10.2969/jmsj/82258225","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49035489","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: 1
Extremal trigonal fibrations on rational surfaces 有理表面上的极端三角颤动
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-11-01 DOI: 10.2969/jmsj/82438243
C. Gong, S. Kitagawa, Jun Lu
{"title":"Extremal trigonal fibrations on rational surfaces","authors":"C. Gong, S. Kitagawa, Jun Lu","doi":"10.2969/jmsj/82438243","DOIUrl":"https://doi.org/10.2969/jmsj/82438243","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41402088","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
On the first eigenvalue of the Laplacian on compact surfaces of genus three 关于亏格三的紧致曲面上拉普拉斯算子的第一特征值
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-10-28 DOI: 10.2969/jmsj/85898589
A. Ros
{"title":"On the first eigenvalue of the Laplacian on compact surfaces of genus three","authors":"A. Ros","doi":"10.2969/jmsj/85898589","DOIUrl":"https://doi.org/10.2969/jmsj/85898589","url":null,"abstract":"For any compact riemannian surface of genus three $(Sigma,ds^2)$ Yang and Yau proved that the product of the first eigenvalue of the Laplacian $lambda_1(ds^2)$ and the area $Area(ds^2)$ is bounded above by $24pi$. In this paper we improve the result and we show that $lambda_1(ds^2)Area(ds^2)leq16(4-sqrt{7})pi approx 21.668,pi$. About the sharpness of the bound, for the hyperbolic Klein quartic surface numerical computations give the value $approx 21.414,pi$.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45167362","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
Systolic inequalities, Ginzburg dg algebras and Milnor fibers 收缩不等式、Ginzburg-dg代数和Milnor纤维
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-10-05 DOI: 10.2969/jmsj/85878587
Jongmyeong Kim
{"title":"Systolic inequalities, Ginzburg dg algebras and Milnor fibers","authors":"Jongmyeong Kim","doi":"10.2969/jmsj/85878587","DOIUrl":"https://doi.org/10.2969/jmsj/85878587","url":null,"abstract":"We prove categorical systolic inequalities for the derived categories of 2-Calabi-Yau Ginzburg dg algebras associated to ADE quivers and explore their symplecto-geometric aspects.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47069698","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
Trivializing group actions on braided crossed tensor categories and graded braided tensor categories 编织交叉张量范畴和渐变编织张量范畴上群作用的琐碎化
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-10-02 DOI: 10.2969/jmsj/85768576
César Galindo
{"title":"Trivializing group actions on braided crossed tensor categories and graded braided tensor categories","authors":"César Galindo","doi":"10.2969/jmsj/85768576","DOIUrl":"https://doi.org/10.2969/jmsj/85768576","url":null,"abstract":"For an abelian group $ A $, we study a close connection between braided crossed $ A $-categories with a trivialization of the $ A $-action and $ A $-graded braided tensor categories. Additionally, we prove that the obstruction to the existence of a trivialization of a categorical group action $T$ on a monoidal category $mathcal{C}$ is given by an element $O(T)in H^2(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$. In the case that $O(T)=0$, the set of obstructions form a torsor over $operatorname{Hom}(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$, where $operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}})$ is the abelian group of tensor natural automorphisms of the identity. \u0000The cohomological interpretation of trivializations, together with the homotopical classification of (faithfully graded) braided $A$-crossed tensor categories developed in arXiv:0909.3140, allows us to provide a method for the construction of faithfully $A$-graded braided tensor categories. We work out two examples. First, we compute the obstruction to the existence of trivializations for the braided crossed category associated with a pointed semisimple tensor category. In the second example, we compute explicit formulas for the braided $mathbb{Z}/2$-crossed structures over Tambara-Yamagami fusion categories and, consequently, a conceptual interpretation of the results in arXiv:math/0011037 about the classification of braidings over Tambara-Yamagami categories.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43538658","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
Poincaré inequalities with exact missing terms on homogeneous groups 齐次群上精确缺项的poincarcars不等式
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2020-10-01 DOI: 10.2969/jmsj/83738373
T. Ozawa, D. Suragan
{"title":"Poincaré inequalities with exact missing terms on homogeneous groups","authors":"T. Ozawa, D. Suragan","doi":"10.2969/jmsj/83738373","DOIUrl":"https://doi.org/10.2969/jmsj/83738373","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47752995","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
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