发布求助
文献互助 智能选刊 最新文献

Calculus of Variations and Partial Differential Equations最新文献

筛选
英文 中文
Singularities of the hyperbolic elastic flow: convergence, quantization and blow-ups 双曲弹性流的奇点：收敛、量化和炸裂
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-29 DOI: 10.1007/s00526-024-02815-4
Manuel Schlierf
{"title":"Singularities of the hyperbolic elastic flow: convergence, quantization and blow-ups","authors":"Manuel Schlierf","doi":"10.1007/s00526-024-02815-4","DOIUrl":"https://doi.org/10.1007/s00526-024-02815-4","url":null,"abstract":"<p>We study the elastic flow of closed curves and of open curves with clamped boundary conditions in the hyperbolic plane. While global existence and convergence toward critical points for initial data with sufficiently small energy is already known, this study pioneers an investigation into the flow’s singular behavior. We prove a convergence theorem without assuming smallness of the initial energy, coupled with a quantification of potential singularities: Each singularity carries an energy cost of at least 8. Moreover, the blow-ups of the singularities are explicitly classified. A further contribution is an explicit understanding of the singular limit of the elastic flow of <span>(lambda )</span>-figure-eights, a class of curves that previously served in showing sharpness of the energy threshold 16 for the smooth convergence of the elastic flow of closed curves.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Dispersive estimates for 1D matrix Schrödinger operators with threshold resonance 具有阈值共振的一维矩阵薛定谔算子的分散估计
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-24 DOI: 10.1007/s00526-024-02817-2
Yongming Li
{"title":"Dispersive estimates for 1D matrix Schrödinger operators with threshold resonance","authors":"Yongming Li","doi":"10.1007/s00526-024-02817-2","DOIUrl":"https://doi.org/10.1007/s00526-024-02817-2","url":null,"abstract":"<p>We establish dispersive estimates and local decay estimates for the time evolution of non-self-adjoint matrix Schrödinger operators with threshold resonances in one space dimension. In particular, we show that the decay rates in the weighted setting are the same as in the regular case after subtracting a finite rank operator corresponding to the threshold resonances. Such matrix Schrödinger operators naturally arise from linearizing a focusing nonlinear Schrödinger equation around a solitary wave. It is known that the linearized operator for the 1D focusing cubic NLS equation exhibits a threshold resonance. We also include an observation of a favorable structure in the quadratic nonlinearity of the evolution equation for perturbations of solitary waves of the 1D focusing cubic NLS equation.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Weighted fractional Poincaré inequalities via isoperimetric inequalities 通过等周不等式的加权分数波因卡雷不等式
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-22 DOI: 10.1007/s00526-024-02813-6
Kim Myyryläinen, Carlos Pérez, Julian Weigt
{"title":"Weighted fractional Poincaré inequalities via isoperimetric inequalities","authors":"Kim Myyryläinen, Carlos Pérez, Julian Weigt","doi":"10.1007/s00526-024-02813-6","DOIUrl":"https://doi.org/10.1007/s00526-024-02813-6","url":null,"abstract":"<p>Our main result is a weighted fractional Poincaré–Sobolev inequality improving the celebrated estimate by Bourgain–Brezis–Mironescu. This also yields an improvement of the classical Meyers–Ziemer theorem in several ways. The proof is based on a fractional isoperimetric inequality and is new even in the non-weighted setting. We also extend the celebrated Poincaré–Sobolev estimate with <span>(A_p)</span> weights of Fabes–Kenig–Serapioni by means of a fractional type result in the spirit of Bourgain–Brezis–Mironescu. Examples are given to show that the corresponding <span>(L^p)</span>-versions of weighted Poincaré inequalities do not hold for <span>(p&gt;1)</span>.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Extension problem for the fractional parabolic Lamé operator and unique continuation 分数抛物线拉梅算子的扩展问题和唯一续集
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-20 DOI: 10.1007/s00526-024-02807-4
Agnid Banerjee, Soumen Senapati
{"title":"Extension problem for the fractional parabolic Lamé operator and unique continuation","authors":"Agnid Banerjee, Soumen Senapati","doi":"10.1007/s00526-024-02807-4","DOIUrl":"https://doi.org/10.1007/s00526-024-02807-4","url":null,"abstract":"<p>In this paper, we introduce and analyse an explicit formulation of fractional powers of the parabolic Lamé operator and we then study the extension problem associated to such non-local operators. We also study the various regularity properties of solutions to such an extension problem via a transformation as in Ang et al. (Commun Partial Differ Equ 23:371–385, 1998), Alessandrini and Morassi (Commun Partial Differ Equ 26(9–10):1787–1810, 2001), Eller et al. (Nonlinear partial differential equations andtheir applications, North-Holland, Amsterdam, 2002), and Gurtin (in: Truesdell, C. (ed.) Handbuch der Physik, Springer, Berlin, 1972), which reduces the extension problem for the parabolic Lamé operator to another system that resembles the extension problem for the fractional heat operator. Finally in the case when <span>(s ge 1/2)</span>, by proving a conditional doubling property for solutions to the corresponding reduced system followed by a blowup argument, we establish a space-like strong unique continuation result for <span>(mathbb {H}^s textbf{u}=Vtextbf{u})</span>.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Schauder estimates for parabolic equations with degenerate or singular weights 具有退化或奇异权重的抛物方程的 Schauder 估计数
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-20 DOI: 10.1007/s00526-024-02809-2
Alessandro Audrito, Gabriele Fioravanti, Stefano Vita
{"title":"Schauder estimates for parabolic equations with degenerate or singular weights","authors":"Alessandro Audrito, Gabriele Fioravanti, Stefano Vita","doi":"10.1007/s00526-024-02809-2","DOIUrl":"https://doi.org/10.1007/s00526-024-02809-2","url":null,"abstract":"<p>We establish some <span>(C^{0,alpha })</span> and <span>(C^{1,alpha })</span> regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane <span>(Sigma )</span> as a power <span>(a &gt; -1)</span> of the distance to <span>(Sigma )</span>. The estimates we obtain are sharp with respect to the assumptions on coefficients and data. Our methods rely on a regularization of the equation and some uniform regularity estimates combined with a Liouville theorem and an approximation argument. As a corollary of our main result, we obtain similar <span>(C^{1,alpha })</span> estimates when the degeneracy/singularity of the weight occurs on a regular hypersurface of cylindrical type.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Interior Hölder estimate for the linearized complex Monge–Ampère equation 线性化复蒙日-安培方程的内部荷尔德估计
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-20 DOI: 10.1007/s00526-024-02814-5
Yulun Xu
{"title":"Interior Hölder estimate for the linearized complex Monge–Ampère equation","authors":"Yulun Xu","doi":"10.1007/s00526-024-02814-5","DOIUrl":"https://doi.org/10.1007/s00526-024-02814-5","url":null,"abstract":"<p>Let <span>(w_0)</span> be a bounded, <span>(C^3)</span>, strictly plurisubharmonic function defined on <span>(B_1subset mathbb {C}^n)</span>. Then <span>(w_0)</span> has a neighborhood in <span>(L^{infty }(B_1))</span>. Suppose that we have a function <span>(phi )</span> in this neighborhood with <span>(1-varepsilon le MA(phi )le 1+varepsilon )</span> and there exists a function <i>u</i> solving the linearized complex Monge–Amp<span>(grave{text {e}})</span>re equation: <span>(det(phi _{kbar{l}})phi ^{ibar{j}}u_{ibar{j}}=0)</span>. Then there exist constants <span>(alpha &gt;0)</span> and <i>C</i> such that <span>(|u|_{C^{alpha }(B_{frac{1}{2}}(0))}le C)</span>, where <span>(alpha &gt;0)</span> depends on <i>n</i> and <i>C</i> depends on <i>n</i> and <span>(|u|_{L^{infty }(B_1(0))})</span>, as long as <span>(epsilon )</span> is small depending on <i>n</i>. This partially generalizes Caffarelli–Gutierrez’s estimate for linearized real Monge–Amp<span>(grave{text {e}})</span>re equation to the complex version.\u0000</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Sharp Sobolev inequalities on noncompact Riemannian manifolds with $$textsf{Ric}ge 0$$ via optimal transport theory 通过最优传输理论在$textsf{Ric}ge 0$$ 的非紧凑黎曼流形上实现尖锐索波列夫不等式
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-17 DOI: 10.1007/s00526-024-02810-9
Alexandru Kristály
{"title":"Sharp Sobolev inequalities on noncompact Riemannian manifolds with $$textsf{Ric}ge 0$$ via optimal transport theory","authors":"Alexandru Kristály","doi":"10.1007/s00526-024-02810-9","DOIUrl":"https://doi.org/10.1007/s00526-024-02810-9","url":null,"abstract":"<p>In their seminal work, Cordero-Erausquin, Nazaret and Villani (Adv Math 182(2):307-332, 2004) proved sharp Sobolev inequalities in Euclidean spaces via <i>Optimal Transport</i>, raising the question whether their approach is powerful enough to produce sharp Sobolev inequalities also on Riemannian manifolds. By using <span>(L^1)</span>-optimal transport approach, the compact case has been successfully treated by Cavalletti and Mondino (Geom Topol 21:603-645, 2017), even on metric measure spaces verifying the synthetic lower Ricci curvature bound. In the present paper we affirmatively answer the above question for noncompact Riemannian manifolds with non-negative Ricci curvature; namely, by using Optimal Transport theory with quadratic distance cost, sharp <span>(L^p)</span>-Sobolev and <span>(L^p)</span>-logarithmic Sobolev inequalities (both for <span>(p&gt;1)</span> and <span>(p=1)</span>) are established, where the sharp constants contain the <i>asymptotic volume ratio</i> arising from precise asymptotic properties of the Talentian and Gaussian bubbles, respectively. As a byproduct, we give an alternative, elementary proof to the main result of do Carmo and Xia (Math 140:818-826, 2004) and subsequent results, concerning the quantitative volume non-collapsing estimates on Riemannian manifolds with non-negative Ricci curvature that support Sobolev inequalities.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Hessian estimates for the Lagrangian mean curvature flow 拉格朗日平均曲率流的赫斯估计值
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-17 DOI: 10.1007/s00526-024-02812-7
Arunima Bhattacharya, Jeremy Wall
{"title":"Hessian estimates for the Lagrangian mean curvature flow","authors":"Arunima Bhattacharya, Jeremy Wall","doi":"10.1007/s00526-024-02812-7","DOIUrl":"https://doi.org/10.1007/s00526-024-02812-7","url":null,"abstract":"<p>In this paper, we prove interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow under the assumption that the Lagrangian phase is hypercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Multiple solutions for (p, q)-Laplacian equations in $$mathbb {R}^N$$ with critical or subcritical exponents 具有临界或亚临界指数的 $$mathbb {R}^N$$ 中 (p, q) - 拉普拉斯方程的多重解
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-14 DOI: 10.1007/s00526-024-02811-8
Shibo Liu, Kanishka Perera
{"title":"Multiple solutions for (p, q)-Laplacian equations in $$mathbb {R}^N$$ with critical or subcritical exponents","authors":"Shibo Liu, Kanishka Perera","doi":"10.1007/s00526-024-02811-8","DOIUrl":"https://doi.org/10.1007/s00526-024-02811-8","url":null,"abstract":"<p>In this paper we study the following <span>(left( p,qright) )</span>-Laplacian equation with critical exponent </p><span>$$begin{aligned} -Delta _{p}u-Delta _{q}u=lambda h(x)|u|^{r-2}u+g(x)|u|^{p^{*} -2}u quad text {in }mathbb {R}^{N} , end{aligned}$$</span><p>where <span>(1&lt;qle p&lt;r&lt;p^{*})</span>. After establishing <span>((PS)_c)</span> condition for <span>(cin (0,c^*))</span> for a certain constant <span>(c^*)</span> by employing the concentration compactness principle of Lions, multiple solutions for <span>(lambda gg 1)</span> are obtained by applying a critical point theorem due to Perera (J Anal Math, 2023. arxiv:2308.07901). A similar problem with subcritical exponents is also considered.</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 effects of long-range interaction to wave propagation 长程相互作用对波传播的影响
IF 2.1 2区 数学
Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-05 DOI: 10.1007/s00526-024-02783-9
Chao-Nien Chen, Yung-Sze Choi, Chih-Chiang Huang, Shyuh-yaur Tzeng
{"title":"The effects of long-range interaction to wave propagation","authors":"Chao-Nien Chen, Yung-Sze Choi, Chih-Chiang Huang, Shyuh-yaur Tzeng","doi":"10.1007/s00526-024-02783-9","DOIUrl":"https://doi.org/10.1007/s00526-024-02783-9","url":null,"abstract":"<p>The mechanisms responsible for pattern formation have attracted a great deal of attention since Alan Turing elucidated his fascinating idea on diffusion-induced instability of steady states. Subsequent studies on the models demonstrated an entirely different class of solutions; namely localized structures composing of steadily moving fronts and pulses. In such energy-driven motion, the combination of short and long-range interaction plays an important ingredient for the generation of complex patterns. This competition on traveling wave dynamics, commonly observed in many physical and chemical phenomena, will be highlighted.\u0000</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信