{"title":"An elliptic equation with random potential and supercritical nonlinearity","authors":"L. Cioletti, L. Ferreira, M. Furtado","doi":"10.18273/REVINT.V37N1-2019001","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019001","url":null,"abstract":"espanolEstamos interesados en una ecuacion eliptica no homogenea con potencial aleatorio y no linealidad supercritica. Obtenemos la existencia de solucion casi seguramente para una clase de potenciales que incluye continuos y discretos. Ademas, proporcionamos una ley de grandes numeros para las soluciones obtenidas por conjuntos independientes y estimamos el valor esperado para sus normas L∞. EnglishWe are concerned with a nonhomogeneous elliptic equation with random potential and supercritical nonlinearity. Existence of solution is obtained almost surely for a class of potentials that includes continuum and discrete ones. Also, we provide a law of larger numbers for the obtained solutions by independent ensembles and estimate the expected value for their L∞-norms.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121397257","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":"On the existence of a priori bounds for positive solutions of elliptic problems, I","authors":"R. Pardo","doi":"10.18273/REVINT.V37N1-2019005","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019005","url":null,"abstract":"espanolContinuamos estudiando la existencia de cotas uniformes a priori para soluciones positivas de equaciones elipticas subcriticas (P)p − Delta_pu = f(u), en Omega, u = 0, sobre ∂Omega, Proporcionamos condiciones suficientes para que las soluciones positivas en C1,μ (overline{Omega }) de una clase de problemas elipticos subcriticos tengan cotas a-priori L∞ en dominios acotados, convexos, y de clase C2. En esta parte II, extendemos nuestros resultados a sistemas elipticos Hamiltonianos −Delta u = f(v), −Delta v = g(u), en Omega , u = v = 0 sobre ∂ Omega, cuando f(v) = vp/[ln(e + v)]α, g(u) = uq/[ln(e + u)]β, con α, β > 2/(N − 2), y p, q varian sobre la hiperbola critica de Sobolev 1/p+1 + 1/q+1 = N−2/N . Para ecuaciones elipticas cuasilineales que involucran al operador p-Laplacian, existen cotas a-priori para soluciones positivas de (P)p en el espacio C1,μ(overline {Omega }), μ ∈ (0, 1), cuando f(u) = up⋆−1/[ln(e + u)]α, con p∗ = Np/(N − p), y α > p/(N − p). Tambien estudiamos el comportamiento asintotico de soluciones radialmente simetric uα = uα(r) de (P)2 cuando α → 0. EnglishWe continue studying the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations(P)p − Delta_pu = f(u), in Omega, u = 0, on ∂Omega,We provide sufficient conditions for having a-priori L∞ bounds for C1,μ (overline{Omega }) positive solutions to a class of subcritical elliptic problems in bounded, convex, C2 domains. In this part II, we extend our results to Hamiltonian elliptic systems −Delta u = f(v),−Deltav = g(u), in Omega, u = v = 0 on ∂Omega, when f(v) = vp /[ln(e + v)]α, g(u) = uq/[ln(e + u)]β, with α, β > 2/(N − 2), and p, q are lying in the critical Sobolev hyperbolae 1/p+1 + 1/q+1 = N−2/N . For quasilinear elliptic equations involving the p-Laplacian, there exists a-priori bounds for positive solutions of (P)p when f(u) = up⋆−1/[ln(e + u)]α, with p∗ = Np/(N−p), and α > p/(N−p). We also study the asymptotic behavior of radially symmetric solutions uα = uα(r) of (P)2 as α → 0.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133973572","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":"Traditional continuum theory arising in inverse limits with set-valued functions","authors":"W. Ingram, Rolla MissouriUSA. Emeritus","doi":"10.18273/REVINT.V37N1-2019003","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019003","url":null,"abstract":"espanolEn los anos desde su introduccion en 2004, casi 100 articulos y libros han sido escritos sobre limites inversos con funciones multivaluadas. Aunque tales limites inversos no siempre producen continuos, muchos aspectosde la teoria clasica de los continuos aparecen en las investigaciones de estos objetos interesantes. En este articulo discutimos varios de los temas tradicionales que han surgido en el estudio de este tema. EnglishIn the years since their introduction in 2004, almost 100 articles and books have been written on the subject of inverse limits with set-valued functions. Although such inverse limits do not always produce continua, much traditional continuum theory arises in investigations of these interesting objects. In this survey article we discuss several tradtional topics that have arisen in research into the subject.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134335228","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":"Continuous images of hereditarily indecomposable continua","authors":"D. Bellamy","doi":"10.18273/REVINT.V37N1-2019007","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019007","url":null,"abstract":"espanolEl teorema demostrado es que todo continuo metrico es imagen continua de algun continuo metrico hereditariamente indescomponible. EnglishThe theorem proven here is that every compact metric continuum is a continuous image of some hereditarily indecomposable metric continuum.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129084110","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":"The property of Kelley and continua","authors":"S. Macías","doi":"10.18273/REVINT.V37N1-2019002","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019002","url":null,"abstract":"espanolEstudiamos a los continuos de Hausdorff con la propiedad de Kelley. Presentamos la version para continuos de Hausdorff de varios resultados conocidos en el caso metrico. Establecemos una version debil de Hausdorff del Teorema de Descomposicion Aposindetica de Jones. EnglishWe study Hausdorff continua with the property of Kelley. We present Hausdorff version of several results known in the metric case. We also establish a weak Hausdorff version of Jones’ Aposyndetic Decomposition Theorem.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123934818","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}
E. León-Cardenal, Zacatecas México. Centro de Investigación en Matemáticas, W. A. Zúñiga-Galindo
{"title":"An Introduction to the Theory of Local Zeta Functions from Scratch","authors":"E. León-Cardenal, Zacatecas México. Centro de Investigación en Matemáticas, W. A. Zúñiga-Galindo","doi":"10.18273/REVINT.V37N1-2019004","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019004","url":null,"abstract":"espanolEn este articulo panoramico brindamos una introduccion a la teoria de las funciones zeta locales p-adicas para principiantes. Tambien se presenta una revision extensiva a la literatura especializada sobre funciones zeta locales y sus conexiones con otros campos de las matematicas y la fisica. EnglishThis survey article aims to provide an introduction to the theory of local zeta functions in the p-adic framework for beginners. We also give an extensive guide to the current literature on local zeta functions and its connections with other fields in mathematics and physics.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122606303","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":"Ideals on countable sets: a survey with questions","authors":"Carlos Enrique Uzcátegui Aylwin","doi":"10.18273/REVINT.V37N1-2019009","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019009","url":null,"abstract":"espanolUn ideal sobre un conjunto X es una coleccion de subconjuntos de X cerrada bajo las operaciones de tomar uniones finitas y subconjuntos de sus elementos. Los ideales son una nocion muy util en topologia y teoriade conjuntos y han sido estudiados desde hace mucho tiempo. Presentamos una revision de algunos resultados sobre ideales en conjuntos numerables incluyendo preguntas abiertas sobre este tema. EnglishAn ideal on a set X is a collection of subsets of X closed under the operations of taking finite unions and subsets of its elements. Ideals are a very useful notion in topology and set theory and have been studied for a long time. We present a survey of results about ideals on countable sets and include many open questions.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128202839","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":"Group algebras and coding theory: a short survey","authors":"C. P. Milies","doi":"10.18273/REVINT.V37N1-2019008","DOIUrl":"https://doi.org/10.18273/REVINT.V37N1-2019008","url":null,"abstract":"espanolEstudiamos codigos construidos a partir de ideales de algebras de grupo y estamos particularmente interesados en sus dimensiones y pesos. Introducimos inicialmente un tipo especial de idempotentes y estudiamos los ideales que generan. Usamos esta informacion para mostrar que existen grupos abelianos no ciclicos que son mas convenientes que los ciclicos. Finalmente, discutimos brevemente algunos resultados sobre codigos no abelianos. EnglishWe study codes constructed from ideals in group algebras and we are particularly interested in their dimensions and weights. First we introduced a special kind of idempotents and study the ideals they generate.We use this information to show that there exist abelian non-cyclic groups that give codes which are more convenient than the cyclic ones. Finally, we discuss briefly some facts about non-abelian codes.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129154788","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":"The asymptotic analysis of a Darcy-Stokessystem coupled through a curved interface","authors":"Fernando A. Morales","doi":"10.18273/REVINT.V37N2-2019004","DOIUrl":"https://doi.org/10.18273/REVINT.V37N2-2019004","url":null,"abstract":"We present the asymptotic analysis of a Darcy-Stokes coupledsystem, modeling the fluid exchange between a narrow channel(Stokes flow)and a porous medium (Darcy flow), coupled through aC2curved interface.The channel is a cylindrical domain between the interface (Γ) and a paralleltranslation of itself (Γ +ǫbeN, ǫ >0). The introduction of a change variable(to fix the domain geometry) and the introduction of two systems of coor-dinates: the Cartesian and a local one (consistent with the geometry of thesurface), permit to find the limiting form of the system when the width of thechannel tends to zero (ǫ→0). The limit problem is a coupled system withDarcy flow in the porous medium and Brinkman flow on the curved interface(Γ).","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121485740","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":"On the existence of a priori bounds forpositive solutions of elliptic problems, II","authors":"R. Pardo","doi":"10.18273/revint.v37n1-2019006","DOIUrl":"https://doi.org/10.18273/revint.v37n1-2019006","url":null,"abstract":"","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123696227","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}