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Milan Journal of Mathematics最新文献

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On a Serrin Type Overdetermined Problem 关于塞林型超决问题
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-09-06 DOI: 10.1007/s00032-024-00405-9
A. Celentano, C. Nitsch, C. Trombetti
{"title":"On a Serrin Type Overdetermined Problem","authors":"A. Celentano, C. Nitsch, C. Trombetti","doi":"10.1007/s00032-024-00405-9","DOIUrl":"https://doi.org/10.1007/s00032-024-00405-9","url":null,"abstract":"<p>In this paper, we prove a Serrin-type result for an elliptic system of equations, overdetermined with both Dirichlet and generalized Neumann conditions. With this tool, we characterize the critical shapes of some domain functionals under volume constraints.\u0000</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Inverse Design and Boundary Controllability for the Chromatography System 色谱系统的逆向设计和边界可控性
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-09-04 DOI: 10.1007/s00032-024-00402-y
Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru
{"title":"Inverse Design and Boundary Controllability for the Chromatography System","authors":"Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru","doi":"10.1007/s00032-024-00402-y","DOIUrl":"https://doi.org/10.1007/s00032-024-00402-y","url":null,"abstract":"<p>We consider the prototypical example of the <span>(2times 2)</span> liquid chromatography system and characterize the set of initial data leading to a given attainable profile at <span>(t=T)</span>. For profiles that are not attainable at time <i>T</i>, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the <span>(L^2)</span>-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz–Kranzer system.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Remarks on Regularization by Noise, Convex Integration and Spontaneous Stochasticity 关于噪声正则化、凸积分和自发随机性的评论
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-09-02 DOI: 10.1007/s00032-024-00406-8
Franco Flandoli, Marco Rehmeier
{"title":"Remarks on Regularization by Noise, Convex Integration and Spontaneous Stochasticity","authors":"Franco Flandoli, Marco Rehmeier","doi":"10.1007/s00032-024-00406-8","DOIUrl":"https://doi.org/10.1007/s00032-024-00406-8","url":null,"abstract":"<p>This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of them deal with the effect on large scales of a small-scale perturbation of fluid dynamic equations. The effects sometimes have something in common, like convex integration and spontaneous stochasticity, sometimes they look the opposite, as in regularization by noise. We are not aware of rigorous links or precise explanations of the differences, and hope to drive new research with this comparative examination.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Representation Theory and Differential Equations 表示理论和微分方程
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-08-22 DOI: 10.1007/s00032-024-00399-4
Ahmed Sebbar, Oumar Wone
{"title":"Representation Theory and Differential Equations","authors":"Ahmed Sebbar, Oumar Wone","doi":"10.1007/s00032-024-00399-4","DOIUrl":"https://doi.org/10.1007/s00032-024-00399-4","url":null,"abstract":"<p>We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated with the cyclic group <span>(mathbb Z/3mathbb Z)</span>, <span>(displaystyle Delta _3=dfrac{partial ^3}{partial x^3}+dfrac{partial ^3}{partial y^3}+dfrac{partial ^3}{partial z^3}-3dfrac{partial ^3}{partial xpartial ypartial z})</span>. This operator appears as a natural extension of the Laplacian in dimension 2. Another originality of our work is to show that the spectral theory of operators associated with Frobenius determinants is closely linked to finite Fourier transform theory.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Proper Direct Image in o-Minimal Expansions of Groups 论群的 o 最小展开中的适当直接映像
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s00032-024-00404-w
Mário J. Edmundo, Luca Prelli
{"title":"On Proper Direct Image in o-Minimal Expansions of Groups","authors":"Mário J. Edmundo, Luca Prelli","doi":"10.1007/s00032-024-00404-w","DOIUrl":"https://doi.org/10.1007/s00032-024-00404-w","url":null,"abstract":"<p>We show that the formalism of the six Grothendieck operations holds in the sub-category of definably locally closed definable subsets equipped with the o-minimal site in o-minimal expansions of ordered groups.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Automorphisms and Twisted Forms of Rings of Invariants 无常环的自变形和扭曲形式
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-07-29 DOI: 10.1007/s00032-024-00403-x
János Kollár
{"title":"Automorphisms and Twisted Forms of Rings of Invariants","authors":"János Kollár","doi":"10.1007/s00032-024-00403-x","DOIUrl":"https://doi.org/10.1007/s00032-024-00403-x","url":null,"abstract":"<p>Let <span>(Gsubset textrm{GL}_n(k))</span> be a finite subgroup and <span>(k[x_1,dots , x_n]^Gsubset k[x_1,dots , x_n])</span> its ring of invariants. We show that, in many cases, the automorphism group of <span>(k[x_1,dots , x_n]^G)</span> is <span>(k^times )</span>.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Positive Solutions of Elliptic Systems with Superlinear Terms on the Critical Hyperbola 临界双曲线上带有超线性项的椭圆系统的正解
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-07-05 DOI: 10.1007/s00032-024-00401-z
Mabel Cuesta, Rosa Pardo, Angela Pistoia
{"title":"Positive Solutions of Elliptic Systems with Superlinear Terms on the Critical Hyperbola","authors":"Mabel Cuesta, Rosa Pardo, Angela Pistoia","doi":"10.1007/s00032-024-00401-z","DOIUrl":"https://doi.org/10.1007/s00032-024-00401-z","url":null,"abstract":"<p>We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type nonlinearities. Instead, we use the dual method on Orlicz spaces, showing that our problem possesses a mountain pass type solution.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Simple Approach to a Dirichlet Problem Related to the Kardar-Parisi-Zhang Equation with Singular Coefficients 解决与具有奇异系数的卡尔达-帕里什-张方程相关的德里赫特问题的简单方法
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-06-08 DOI: 10.1007/s00032-024-00400-0
Lucio Boccardo, Pasquale Imparato
{"title":"A Simple Approach to a Dirichlet Problem Related to the Kardar-Parisi-Zhang Equation with Singular Coefficients","authors":"Lucio Boccardo, Pasquale Imparato","doi":"10.1007/s00032-024-00400-0","DOIUrl":"https://doi.org/10.1007/s00032-024-00400-0","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141370546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The Role of Convection in the Limit Shape of the Critical Front Profile for Born-Infeld Diffusion Models 对流在 Born-Infeld 扩散模型临界前沿剖面极限形状中的作用
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00032-024-00397-6
Maurizio Garrione, Mohamed Jleli, Bessem Samet
{"title":"The Role of Convection in the Limit Shape of the Critical Front Profile for Born-Infeld Diffusion Models","authors":"Maurizio Garrione, Mohamed Jleli, Bessem Samet","doi":"10.1007/s00032-024-00397-6","DOIUrl":"https://doi.org/10.1007/s00032-024-00397-6","url":null,"abstract":"<p>In this paper, we deal with models with <i>Born-Infeld</i> (or <i>relativistic</i>) type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equivalent first-order problem, we show that different convection terms may lead either to a complete sharpening of the limit profile or to its complete regularization, presenting some related numerical simulations.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Layered Patterns in Reaction–Diffusion Models with Perona–Malik Diffusions 带有佩罗纳-马利克扩散的反应-扩散模型中的分层模式
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00032-024-00398-5
Alessandra De Luca, Raffaele Folino, Marta Strani
{"title":"Layered Patterns in Reaction–Diffusion Models with Perona–Malik Diffusions","authors":"Alessandra De Luca, Raffaele Folino, Marta Strani","doi":"10.1007/s00032-024-00398-5","DOIUrl":"https://doi.org/10.1007/s00032-024-00398-5","url":null,"abstract":"<p>In this paper we deal with a reaction–diffusion equation in a bounded interval of the real line with a nonlinear diffusion of Perona–Malik’s type and a balanced bistable reaction term. Under very general assumptions, we study the persistence of layered solutions, showing that it strongly depends on the behavior of the reaction term close to the stable equilibria <span>(pm 1)</span>, described by a parameter <span>(theta &gt;1)</span>. If <span>(theta in (1,2))</span>, we prove existence of steady states oscillating (and touching) <span>(pm 1)</span>, called <i>compactons</i>, while in the case <span>(theta =2)</span> we prove the presence of <i>metastable solutions</i>, namely solutions with a transition layer structure which is maintained for an exponentially long time. Finally, for <span>(theta &gt;2)</span>, solutions with an unstable transition layer structure persist only for an algebraically long time.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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