应用数学年刊:英文版Pub Date : 2021-06-01DOI: 10.4208/aam.oa-2021-0006
Dong Li
{"title":"On Fractional Smoothness of Modulus of Functions","authors":"Dong Li","doi":"10.4208/aam.oa-2021-0006","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0006","url":null,"abstract":"We consider the Nemytskii operators $uto |u|$ and $uto u^{pm}$ in a bounded domain $Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(Omega)$ with $0le s<3/2$.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42480540","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}
应用数学年刊:英文版Pub Date : 2021-06-01DOI: 10.4208/aam.oa-2021-0007
global sci
{"title":"High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows","authors":"global sci","doi":"10.4208/aam.oa-2021-0007","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0007","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42675372","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}
应用数学年刊:英文版Pub Date : 2021-04-22DOI: 10.4208/aam.oa-2021-0004
R. Chen, Jie Jin
{"title":"Transverse Instability of the CH-KP-I Equation","authors":"R. Chen, Jie Jin","doi":"10.4208/aam.oa-2021-0004","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0004","url":null,"abstract":"The Camassa–Holm–Kadomtsev–Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa–Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse perturbations. The proof is based on the framework of [18]. Due to the high nonlinearity, our proof requires necessary modification. Specifically, we first establish the linear instability of the line solitary waves. Then through an approximation procedure, we prove that the linear effect actually dominates the nonlinear behavior.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45009304","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}
应用数学年刊:英文版Pub Date : 2021-04-14DOI: 10.4208/aam.oa-2022-0001
Jingzhi Li, Hongyu Liu, Lan Tang, Jiangwen Wang
{"title":"Boundary Homogenization of a Class of Obstacle Problems","authors":"Jingzhi Li, Hongyu Liu, Lan Tang, Jiangwen Wang","doi":"10.4208/aam.oa-2022-0001","DOIUrl":"https://doi.org/10.4208/aam.oa-2022-0001","url":null,"abstract":"We study homogenization of a boundary obstacle problem on C domain D for some elliptic equations with uniformly elliptic coefficient matrices γ. For any ǫ ∈ R+, ∂D = Γ ∪ Σ, Γ ∩ Σ = ∅ and Sǫ ⊂ Σ with suitable assumptions, we prove that as ǫ tends to zero, the energy minimizer u of ∫ D |γ∇u|dx, subject to u ≥ φ on Sε, up to a subsequence, converges weakly in H(D) to ũ which minimizes the energy functional ∫ D |γ∇u| + ∫ Σ (u− φ)−μ(x)dSx, where μ(x) depends on the structure of Sǫ and φ is any given function in C∞(D).","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48415158","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}
应用数学年刊:英文版Pub Date : 2020-12-05DOI: 10.4208/aam.oa-2021-0002
Jinxin Xue
{"title":"KAM and Geodesic Dynamics of Blackholes","authors":"Jinxin Xue","doi":"10.4208/aam.oa-2021-0002","DOIUrl":"https://doi.org/10.4208/aam.oa-2021-0002","url":null,"abstract":"In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply mainly to two observable phenomena: the photon shell (unstable bound spherical orbits) and the quasi-periodic oscillations. We discover there is a gap structure in the photon shell that can be used to reveal information of the perturbation.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48804087","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}
应用数学年刊:英文版Pub Date : 2020-07-06DOI: 10.4208/aam.OA-2022-0008
T. Jiang, Zilin Jiang, Jie Ma
{"title":"Negligible Obstructions and Turán Exponents","authors":"T. Jiang, Zilin Jiang, Jie Ma","doi":"10.4208/aam.OA-2022-0008","DOIUrl":"https://doi.org/10.4208/aam.OA-2022-0008","url":null,"abstract":"We show that for every rational number $r in (1,2)$ of the form $2 - a/b$, where $a, b in mathbb{N}^+$ satisfy $lfloor a/b rfloor^3 le a le b / (lfloor b/a rfloor +1) + 1$, there exists a graph $F_r$ such that the Turan number $operatorname{ex}(n, F_r) = Theta(n^r)$. Our result in particular generates infinitely many new Turan exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41920679","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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