The main purpose of this article is to establish the existence result concerning to the problem −Δu(x )+ c(x)u(x )= a(x)f (u(x)), x ∈ R N , N> 2, u(x) → 0a s|x |→∞ . Similary problems have been also studied. The proofs of the existence are based on the maximum principle and sub and super solutions method.
本文的主要目的是建立关于−Δu(x)+ c(x)u(x)= a(x)f (u(x))， x∈rn, N >2, u(x)→0a s|x |→∞问题的存在性结果。类似的问题也被研究过。存在性的证明是基于极大值原理和上、下解方法。
{"title":"A Lane-Emden-Fowler type problem with singular nonlinearity","authors":"D. Covei","doi":"10.1215/KJM/1256219159","DOIUrl":"https://doi.org/10.1215/KJM/1256219159","url":null,"abstract":"The main purpose of this article is to establish the existence result concerning to the problem −Δu(x )+ c(x)u(x )= a(x)f (u(x)), x ∈ R N , N> 2, u(x) → 0a s|x |→∞ . Similary problems have been also studied. The proofs of the existence are based on the maximum principle and sub and super solutions method.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113650","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}
We obtain the tail estimation of the quadratic variation of a local martingale with no assumption with respect to positive jumps. Moreover, applying it, we also discuss a tail property of the first-passage times of stochastic integrals.
{"title":"The quadratic variations of local martingales and the first-passage times of stochastic integrals","authors":"S. Kaji","doi":"10.1215/KJM/1260975037","DOIUrl":"https://doi.org/10.1215/KJM/1260975037","url":null,"abstract":"We obtain the tail estimation of the quadratic variation of a local martingale with no assumption with respect to positive jumps. Moreover, applying it, we also discuss a tail property of the first-passage times of stochastic integrals.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1260975037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113952","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}
{"title":"An asymptotic estimate for the hitting time of a half-line by two-dimensional Brownian motion","authors":"Y. Isozaki","doi":"10.1215/KJM/1260975041","DOIUrl":"https://doi.org/10.1215/KJM/1260975041","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1260975041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114075","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}
{"title":"Decaying solution of a Navier-Stokes flow without surface tension","authors":"Yasushi Hataya","doi":"10.1215/KJM/1265899478","DOIUrl":"https://doi.org/10.1215/KJM/1265899478","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1265899478","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114197","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}
We consider a class of linear higher order hyperbolic equations with a single degenerate point. We give sufficient conditions in order for the Cauchy problem to be well-posed in Gevrey classes and in the $C^infty$ class.
{"title":"Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order","authors":"H. Ishida","doi":"10.1215/KJM/1248983035","DOIUrl":"https://doi.org/10.1215/KJM/1248983035","url":null,"abstract":"We consider a class of linear higher order hyperbolic equations with a single degenerate point. We give sufficient conditions in order for the Cauchy problem to be well-posed in Gevrey classes and in the $C^infty$ class.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087650","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}
Dolgopyat [4] showed that a class of Axiom A flows has exponential decay of correlations for smooth observables, and Baladi-Vallée [2] gave a nice interpretation of it on suspension semiflows of one-dimensional expanding countable Markov maps. Avila-Gouëzel-Yoccoz [1] extends the result of Baladi-Vallée to higher dimensional systems. In this paper we show that a class of non-Markov semiflows also has exponential decay of correlations. We prove that such exponential decay can be shown on an open dense condition for the suspensions of piecewise expanding maps.
{"title":"Exponential decay of correlations for surface semiflows with an expanding direction","authors":"I. Obayashi","doi":"10.1215/KJM/1256219166","DOIUrl":"https://doi.org/10.1215/KJM/1256219166","url":null,"abstract":"Dolgopyat [4] showed that a class of Axiom A flows has exponential decay of correlations for smooth observables, and Baladi-Vallée [2] gave a nice interpretation of it on suspension semiflows of one-dimensional expanding countable Markov maps. Avila-Gouëzel-Yoccoz [1] extends the result of Baladi-Vallée to higher dimensional systems. In this paper we show that a class of non-Markov semiflows also has exponential decay of correlations. We prove that such exponential decay can be shown on an open dense condition for the suspensions of piecewise expanding maps.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1256219166","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113888","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}
{"title":"A variational representation for random functionals on abstract Wiener spaces","authors":"Xicheng Zhang","doi":"10.1215/KJM/1260975036","DOIUrl":"https://doi.org/10.1215/KJM/1260975036","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1260975036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113942","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}
We determine the composition factors of the polynomial representation of DAHA, conjectured by M. Kasatani in [Kasa, Conjecture 6.4.]. He constructed an increasing sequence of subrepresentations in the polynomial representation of DAHA using the “multi-wheel condition”, and conjectured that it is a composition series. On the other hand, DAHA has two degenerate versions called the “degenerate DAHA” and the “rational DAHA”. The category O of modules over these three algebras and the category of modules over the v -Schur algebra are closely related. By using this relationship, we reduce the determination of composition factors of polynomial representations of DAHA to the determination of the composition factors of the Weyl module W ( n ) v for the v -Schur algebra. By using the LLT-Ariki type theorem of v -Schur algebra proved by Varagnolo-Vasserot, we determine the composition factors of W ( n ) v by calculating the upper global basis and crystal basis of Fock space of U q ( b sl (cid:2) ) when v is a primitive (cid:2) -th root of unity. This result gives a different way from the determination of decomposition number of W ( n ) v by H. Miyachi or B. Ackermann via the modular representation theory of the general linear groups.
{"title":"Composition factors of polynomial representation of DAHA and q-decomposition numbers","authors":"Naoya Enomoto","doi":"10.1215/KJM/1260975035","DOIUrl":"https://doi.org/10.1215/KJM/1260975035","url":null,"abstract":"We determine the composition factors of the polynomial representation of DAHA, conjectured by M. Kasatani in [Kasa, Conjecture 6.4.]. He constructed an increasing sequence of subrepresentations in the polynomial representation of DAHA using the “multi-wheel condition”, and conjectured that it is a composition series. On the other hand, DAHA has two degenerate versions called the “degenerate DAHA” and the “rational DAHA”. The category O of modules over these three algebras and the category of modules over the v -Schur algebra are closely related. By using this relationship, we reduce the determination of composition factors of polynomial representations of DAHA to the determination of the composition factors of the Weyl module W ( n ) v for the v -Schur algebra. By using the LLT-Ariki type theorem of v -Schur algebra proved by Varagnolo-Vasserot, we determine the composition factors of W ( n ) v by calculating the upper global basis and crystal basis of Fock space of U q ( b sl (cid:2) ) when v is a primitive (cid:2) -th root of unity. This result gives a different way from the determination of decomposition number of W ( n ) v by H. Miyachi or B. Ackermann via the modular representation theory of the general linear groups.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113905","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}
In this paper, we consider the strong unique continuation for normal elliptic systems whose coefficients are Gevrey class. By using Lerner’s lemma, we prove the Carleman estimate with some weight function.
{"title":"A note on strong unique continuation for normal elliptic systems with Gevrey coefficients","authors":"M. Tamura","doi":"10.1215/KJM/1260975040","DOIUrl":"https://doi.org/10.1215/KJM/1260975040","url":null,"abstract":"In this paper, we consider the strong unique continuation for normal elliptic systems whose coefficients are Gevrey class. By using Lerner’s lemma, we prove the Carleman estimate with some weight function.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114063","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}
In [28], Kitchloo constructed a map f : BX → BK∧ p where K is a certain KacMoody group of rank two, X is a rank two mod p finite loop space and f is such that it induces an isomorphism between even dimensional mod p cohomology groups. Here B denotes the classifying space functor and (−)p denotes the Bousfield-Kan Fp-completion functor ([8]). This space X —or rather the triple (X∧ p , BX ∧ p , e) where e : X ' ΩBX— is a particular example of what is known as a p-compact group. These objects were introduced by Dwyer and Wilkerson in [15] as the homotopy theoretical framework to study finite loop spaces and compact Lie groups from a homotopy point of view. The foundational paper [15] together with its many sequels by Dwyer-Wilkerson and other authors represent now an active, well established research area which contains some of the most important recent advances in homotopy theory. While p-compact groups are nowadays reasonably well understood objects, our understanding of Kac-Moody groups and their classifying spaces from a homotopy point of view is far from satisfactory. The work of Kitchloo in [28] started a project which has also involved Broto, Saumell, Ruiz and the present author and has produced a series of results ([2], [3], [10]) which show interesting similarities between this theory and the theory of p-compact groups, as well as non trivial challenging differences. The goal of this paper is to extend the construction of Kitchloo that we have recalled above to produce rank-preserving maps BX → BK∧ p for a wide family of p-compact groups X. These maps can be understood as the homotopy analogues to monomorphisms, in a sense that will be made precise in section 13. We prove:
{"title":"$p$-compact groups as subgroups of maximal rank of Kac-Moody groups","authors":"J. Bover","doi":"10.1215/KJM/1248983031","DOIUrl":"https://doi.org/10.1215/KJM/1248983031","url":null,"abstract":"In [28], Kitchloo constructed a map f : BX → BK∧ p where K is a certain KacMoody group of rank two, X is a rank two mod p finite loop space and f is such that it induces an isomorphism between even dimensional mod p cohomology groups. Here B denotes the classifying space functor and (−)p denotes the Bousfield-Kan Fp-completion functor ([8]). This space X —or rather the triple (X∧ p , BX ∧ p , e) where e : X ' ΩBX— is a particular example of what is known as a p-compact group. These objects were introduced by Dwyer and Wilkerson in [15] as the homotopy theoretical framework to study finite loop spaces and compact Lie groups from a homotopy point of view. The foundational paper [15] together with its many sequels by Dwyer-Wilkerson and other authors represent now an active, well established research area which contains some of the most important recent advances in homotopy theory. While p-compact groups are nowadays reasonably well understood objects, our understanding of Kac-Moody groups and their classifying spaces from a homotopy point of view is far from satisfactory. The work of Kitchloo in [28] started a project which has also involved Broto, Saumell, Ruiz and the present author and has produced a series of results ([2], [3], [10]) which show interesting similarities between this theory and the theory of p-compact groups, as well as non trivial challenging differences. The goal of this paper is to extend the construction of Kitchloo that we have recalled above to produce rank-preserving maps BX → BK∧ p for a wide family of p-compact groups X. These maps can be understood as the homotopy analogues to monomorphisms, in a sense that will be made precise in section 13. We prove:","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087215","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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