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Courant-sharp Robin eigenvalues for the square and other planar domains 正方形和其他平面域的Courant sharp-Robin特征值
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-12-21 DOI: 10.4171/pm/2027
K. Gittins, B. Helffer
{"title":"Courant-sharp Robin eigenvalues for the square and other planar domains","authors":"K. Gittins, B. Helffer","doi":"10.4171/pm/2027","DOIUrl":"https://doi.org/10.4171/pm/2027","url":null,"abstract":"This paper is devoted to the determination of the cases where there is equality in Courant's nodal domain theorem in the case of a Robin boundary condition. For the square, we partially extend the results that were obtained by Pleijel, B'erard--Helffer, Helffer--Persson--Sundqvist for the Dirichlet and Neumann problems. \u0000After proving some general results that hold for any value of the Robin parameter $h$, we focus on the case when $h$ is large. We hope to come back to the analysis when $h$ is small in a second paper. \u0000We also obtain some semi-stability results for the number of nodal domains of a Robin eigenfunction of a domain with $C^{2,alpha}$ boundary ($alpha >0$) as $h$ large varies.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2027","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49625568","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: 7
On flows generated by vector fields with compact support 关于紧支持向量场生成的流
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-12-12 DOI: 10.4171/PM/2013
O. Kneuss, W. Neves
{"title":"On flows generated by vector fields with compact support","authors":"O. Kneuss, W. Neves","doi":"10.4171/PM/2013","DOIUrl":"https://doi.org/10.4171/PM/2013","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PM/2013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45008722","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
Remarks on the Bohnenblust–Hille inequalities 关于bohnenblust - hill不等式的评述
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-11-22 DOI: 10.4171/pm/2040
D. Paulino, D. Pellegrino, Joedson Santos
{"title":"Remarks on the Bohnenblust–Hille inequalities","authors":"D. Paulino, D. Pellegrino, Joedson Santos","doi":"10.4171/pm/2040","DOIUrl":"https://doi.org/10.4171/pm/2040","url":null,"abstract":"We revisit the Bohnenblust--Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of variables.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44254283","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
The universal bound property for a class of second order ODEs 一类二阶常微分方程的泛界性质
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-11-06 DOI: 10.4171/pm/2026
M. Abdelli, A. Haraux
{"title":"The universal bound property for a class of second order ODEs","authors":"M. Abdelli, A. Haraux","doi":"10.4171/pm/2026","DOIUrl":"https://doi.org/10.4171/pm/2026","url":null,"abstract":"We consider the scalar second order ODE u + |u | $alpha$ u + |u| $beta$ u = 0, where $alpha$, $beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 0, u (t) 2 + |u(t)| $beta$+2 $le$ C max{t -- 2 $alpha$ , t -- ($alpha$+1)($beta$+2) $beta$--$alpha$ }.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47242703","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
Fourier approximation methods for first-order nonlocal mean-field games 一阶非局部平均场对策的傅立叶近似方法
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-11-03 DOI: 10.4171/pm/2023
L. Nurbekyan, João Saúde
{"title":"Fourier approximation methods for first-order nonlocal mean-field games","authors":"L. Nurbekyan, João Saúde","doi":"10.4171/pm/2023","DOIUrl":"https://doi.org/10.4171/pm/2023","url":null,"abstract":"In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47403921","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: 18
On minimal Hölder gaps and Shannon entropy balance 关于极小Hölder间隙和Shannon熵平衡
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-07-05 DOI: 10.4171/PM/2009
I. Bomze
{"title":"On minimal Hölder gaps and Shannon entropy balance","authors":"I. Bomze","doi":"10.4171/PM/2009","DOIUrl":"https://doi.org/10.4171/PM/2009","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PM/2009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45192425","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
Ricci flow on cone surfaces 锥面上的利玛窦流
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-07-05 DOI: 10.4171/PM/2010
Daniel Ramos
{"title":"Ricci flow on cone surfaces","authors":"Daniel Ramos","doi":"10.4171/PM/2010","DOIUrl":"https://doi.org/10.4171/PM/2010","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PM/2010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46757981","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: 3
Homogenization of obstacle problems in Orlicz–Sobolev spaces Orlicz-Sobolev空间中障碍问题的均匀化
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-06-22 DOI: 10.4171/pm/2019
Diego Marcon, J. Rodrigues, R. Teymurazyan
{"title":"Homogenization of obstacle problems in Orlicz–Sobolev spaces","authors":"Diego Marcon, J. Rodrigues, R. Teymurazyan","doi":"10.4171/pm/2019","DOIUrl":"https://doi.org/10.4171/pm/2019","url":null,"abstract":"We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(cdot)$-Laplacian type. Our approach is based on the Lewy-Stampacchia inequalities, which then give access to a compactness argument. We also prove the convergence of the coincidence sets under non-degeneracy conditions.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43830125","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
Motivic volumes of fibers of tropicalization 热带化纤维的动力体积
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-05-22 DOI: 10.4171/pm/2045
Jeremy Usatine
{"title":"Motivic volumes of fibers of tropicalization","authors":"Jeremy Usatine","doi":"10.4171/pm/2045","DOIUrl":"https://doi.org/10.4171/pm/2045","url":null,"abstract":"Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$-toric variety such that $U = X cap T$ is not empty, and let $mathscr{L}(X)$ be the arc scheme of $X$. We define a tropicalization map on $mathscr{L}(X) setminus mathscr{L}(X setminus U)$, the set of arcs of $X$ that do not factor through $X setminus U$. We show that each fiber of this tropicalization map is a constructible subset of $mathscr{L}(X)$ and therefore has a motivic volume. We prove that if $U$ has a compactification with simple normal crossing boundary, then the generating function for these motivic volumes is rational, and we express this rational function in terms of certain lattice maps constructed in Hacking, Keel, and Tevelev's theory of geometric tropicalization. We explain how this result, in particular, gives a formula for Denef and Loeser's motivic zeta function of a polynomial. To further understand this formula, we also determine precisely which lattice maps arise in the construction of geometric tropicalization.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42685088","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
Nitsche’s method for unilateral contact problems 单侧接触问题的Nitsche方法
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2018-05-11 DOI: 10.4171/pm/2016
T. Gustafsson, R. Stenberg, J. Videman
{"title":"Nitsche’s method for unilateral contact problems","authors":"T. Gustafsson, R. Stenberg, J. Videman","doi":"10.4171/pm/2016","DOIUrl":"https://doi.org/10.4171/pm/2016","url":null,"abstract":"We derive optimal a priori and a posteriori error estimates for Nitsche's method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche's method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the scalar Signorini problem and outline only the proofs of the main results since most of the auxiliary results can be traced to our previous works on the numerical approximation of variational inequalities. We end the paper by presenting results of our numerical computations which corroborate the efficiency and reliability of the a posteriori estimators.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45670296","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: 8
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