Vietnam Journal of Mathematics最新文献

{"title":"Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part","authors":"Martin Dindoš, Erik Sätterqvist, Martin Ulmer","doi":"10.1007/s10013-023-00653-z","DOIUrl":"https://doi.org/10.1007/s10013-023-00653-z","url":null,"abstract":"Abstract In the present paper we study perturbation theory for the $$L^p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> Dirichlet problem on bounded chord arc domains for elliptic operators in divergence form with potentially unbounded antisymmetric part in BMO. Specifically, given elliptic operators $$L_0 = text {div}(A_0nabla )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mtext>div</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>∇</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and $$L_1 = text {div}(A_1nabla )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mtext>div</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>∇</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> such that the $$L^p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> Dirichlet problem for $$L_0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> is solvable for some $$p&gt;1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ; we show that if $$A_0 - A_1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> satisfies certain Carleson condition, then the $$L^q$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>q</mml:mi> </mml:msup> </mml:math> Dirichlet problem for $$L_1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> is solvable for some $$q ge p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>≥</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> . Moreover if the Carleson norm is small then we may take $$q=p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> . We use the approach first introduced in Fefferman–Kenig–Pipher ’91 on the unit ball, and build on Milakis–Pipher–Toro ’11 where the large norm case was shown for symmetric matrices on bounded chord arc domains. We then apply this to solve the $$L^p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818801","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":"Boundary Value Problems for Elliptic Operators Satisfying Carleson Condition","authors":"Martin Dindoš, Jill Pipher","doi":"10.1007/s10013-023-00650-2","DOIUrl":"https://doi.org/10.1007/s10013-023-00650-2","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135463806","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 Stability of Shear Flows in Bounded Channels, I: Monotonic Shear Flows","authors":"Alexandru D. Ionescu, Hao Jia","doi":"10.1007/s10013-023-00656-w","DOIUrl":"https://doi.org/10.1007/s10013-023-00656-w","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294979","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":"Absolute Exponential Stability Criteria for Some Classes of Nonlinear Time-Varying Systems with Delays and Sector Nonlinearities","authors":"Nguyen Khoa Son, Nguyen Thi Hong","doi":"10.1007/s10013-023-00655-x","DOIUrl":"https://doi.org/10.1007/s10013-023-00655-x","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135253342","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":"Computing the Non-properness Set of Real Polynomial Maps in the Plane","authors":"Boulos El Hilany, Elias Tsigaridas","doi":"10.1007/s10013-023-00652-0","DOIUrl":"https://doi.org/10.1007/s10013-023-00652-0","url":null,"abstract":"Abstract We introduce novel mathematical and computational tools to develop a complete algorithm for computing the set of non-properness of polynomials maps in the plane. In particular, this set, which we call the Jelonek set , is a subset of $$mathbb {K}^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , where a dominant polynomial map $$f: mathbb {K}^2 rightarrow mathbb {K}^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> is not proper; $$mathbb {K}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> could be either $$mathbb {C}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> or $$mathbb {R}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>R</mml:mi> </mml:math> . Unlike all the previously known approaches we make no assumptions on f whenever $$mathbb {K} = mathbb {R}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> ; this is the first algorithm with this property. The algorithm takes into account the Newton polytopes of the polynomials. As a byproduct we provide a finer representation of the set of non-properness as a union of semi-algebraic curves, that correspond to edges of the Newton polytopes, which is of independent interest. Finally, we present a precise Boolean complexity analysis of the algorithm and a prototype implementation in maple .","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135592116","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 Landis’ Conjecture in the Plane for Potentials with Growth","authors":"Blair Davey","doi":"10.1007/s10013-023-00654-y","DOIUrl":"https://doi.org/10.1007/s10013-023-00654-y","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193140","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":"Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation","authors":"Andrew Lawrie","doi":"10.1007/s10013-023-00648-w","DOIUrl":"https://doi.org/10.1007/s10013-023-00648-w","url":null,"abstract":"Abstract In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded $$dot{H} ^1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msup> </mml:math> norm. The proof uses a combination of Gérard’s profile decomposition (ESAIM Control Optim. Calc. Var. 3 : 213–233, 1998), concentration compactness techniques in the spirit of Duyckaerts, Kenig, and Merle’s seminal work (Geom. Funct. Anal. 22 : 639–698, 2012), and a virial argument in the spirit of Jia and Kenig’s work (Amer. J. Math. 139 : 1521–1603, 2017) to deduce the vanishing of the error in the neck regions between the bubbles. The argument is based closely on an analogous lemma proved in the author’s recent work with Jendrej (arXiv:2210.14963, 2022) on the equivariant harmonic map heat flow in dimension two.","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134886841","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 Classical Solutions of the Compressible Euler Equations for Generalized Chaplygin Gas with Qualitative Analysis","authors":"Ka Luen Cheung, Sen Wong","doi":"10.1007/s10013-023-00651-1","DOIUrl":"https://doi.org/10.1007/s10013-023-00651-1","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959719","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":"Extragradient Algorithms with Linesearches for Solving Nonmonotone Equilibrium Problems in Banach Spaces","authors":"B. Dinh, Hy Duc Manh, Tran Thi Huyen Thanh","doi":"10.1007/s10013-023-00649-9","DOIUrl":"https://doi.org/10.1007/s10013-023-00649-9","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45914547","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 Continuity Properties of Solution Maps of the Generalized SQG Family","authors":"G. Misiołek, Xuan-Truong Vu","doi":"10.1007/s10013-023-00647-x","DOIUrl":"https://doi.org/10.1007/s10013-023-00647-x","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44350699","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}