发布求助
文献互助 智能选刊 最新文献

Potential Analysis最新文献

筛选
英文 中文
Stochastic Partial Differential Equations and Invariant Manifolds in Embedded Hilbert Spaces 嵌入希尔伯特空间中的随机偏微分方程和不变曲率
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-05-11 DOI: 10.1007/s11118-024-10134-8
Rajeev Bhaskaran, Stefan Tappe
{"title":"Stochastic Partial Differential Equations and Invariant Manifolds in Embedded Hilbert Spaces","authors":"Rajeev Bhaskaran, Stefan Tappe","doi":"10.1007/s11118-024-10134-8","DOIUrl":"https://doi.org/10.1007/s11118-024-10134-8","url":null,"abstract":"<p>We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth coefficients. Furthermore, we establish a link between invariance of submanifolds for such SPDEs in Hermite Sobolev spaces and invariance of submanifolds for finite dimensional SDEs. This provides a new method for analyzing stochastic invariance of submanifolds for finite dimensional Itô diffusions, which we will use in order to derive new invariance results for finite dimensional SDEs.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927004","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 Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients 论具有时变系数的畸变抛物方程的基本解和高斯边界
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-05-06 DOI: 10.1007/s11118-024-10143-7
Alireza Ataei, Kaj Nyström
{"title":"On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients","authors":"Alireza Ataei, Kaj Nyström","doi":"10.1007/s11118-024-10143-7","DOIUrl":"https://doi.org/10.1007/s11118-024-10143-7","url":null,"abstract":"<p>We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial <span>(A_2)</span>-weight. We prove the existence of a fundamental solution and derive Gaussian bounds. Our construction is based on the original work of Kato (Nagoya Math. J. <b>19</b>, 93–125 1961).</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"222 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886659","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
Marcinkiewicz Estimates for Solutions of Some Elliptic Problems with Singular Data 具有奇异数据的某些椭圆问题解的 Marcinkiewicz 估计数
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-05-03 DOI: 10.1007/s11118-024-10140-w
Lucio Boccardo, Luigi Orsina
{"title":"Marcinkiewicz Estimates for Solutions of Some Elliptic Problems with Singular Data","authors":"Lucio Boccardo, Luigi Orsina","doi":"10.1007/s11118-024-10140-w","DOIUrl":"https://doi.org/10.1007/s11118-024-10140-w","url":null,"abstract":"<p>In this paper we prove regularity result for solutions of the boundary value problem </p><span>$$ left{ begin{array}{cl} -{{,textrm{div},}}(M(x),nabla u) + u = -{{,textrm{div},}}(u,E(x)) + f(x),, &amp;{} text{ in },, Omega , u = 0,, &amp;{} text{ on },,partial Omega , end{array} right. $$</span><p>with the vector field <i>E</i>(<i>x</i>) and the function <i>f</i>(<i>x</i>) belonging to some Marcinkiewicz spaces.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"44 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886572","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
Capacities and Density Conditions in Metric Spaces 公制空间中的容量和密度条件
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-30 DOI: 10.1007/s11118-024-10137-5
Javier Canto, Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas
{"title":"Capacities and Density Conditions in Metric Spaces","authors":"Javier Canto, Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas","doi":"10.1007/s11118-024-10137-5","DOIUrl":"https://doi.org/10.1007/s11118-024-10137-5","url":null,"abstract":"<p>We examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz <span>((beta ,p))</span>-capacity and the relative Hajłasz <span>((beta ,p))</span>-capacity, for <span>(1&lt;p&lt;infty )</span> and <span>(0&lt;beta le 1)</span>, under a suitable kernel estimate related to the Riesz potential. Then we show that in geodesic spaces the corresponding capacity density conditions are equivalent even without assuming the kernel estimate. In the last part of the paper, we compare the relative Hajłasz (1, <i>p</i>)-capacity to the relative variational <i>p</i>-capacity.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"26 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835320","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
Intrinsic Harnack’s Inequality for a General Nonlinear Parabolic Equation in Non-divergence Form 非发散形式一般非线性抛物方程的本征哈纳克不等式
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-25 DOI: 10.1007/s11118-024-10141-9
Tapio Kurkinen, Jarkko Siltakoski
{"title":"Intrinsic Harnack’s Inequality for a General Nonlinear Parabolic Equation in Non-divergence Form","authors":"Tapio Kurkinen, Jarkko Siltakoski","doi":"10.1007/s11118-024-10141-9","DOIUrl":"https://doi.org/10.1007/s11118-024-10141-9","url":null,"abstract":"<p>We prove the intrinsic Harnack’s inequality for a general form of a parabolic equation that generalizes both the standard parabolic <i>p</i>-Laplace equation and the normalized version arising from stochastic game theory. We prove each result for the optimal range of exponents and ensure that we get stable constants.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"66 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800515","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
Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain 双连域上考奇算子及其与伯格曼投影的乘积的谱渐近性
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-19 DOI: 10.1007/s11118-024-10139-3
Djordjije Vujadinović
{"title":"Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain","authors":"Djordjije Vujadinović","doi":"10.1007/s11118-024-10139-3","DOIUrl":"https://doi.org/10.1007/s11118-024-10139-3","url":null,"abstract":"<p>We found the exact asymptotics of the singular numbers for the Cauchy transform and its product with Bergman’s projection over the space <span>(L^{2}(Omega ),)</span> where <span>(Omega )</span> is a doubly-connected domain in the complex plane.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"90 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628580","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
Inclusion Relations Among Fractional Orlicz-Sobolev Spaces and a Littlewood-Paley Characterization 分数奥利兹-索博廖夫空间之间的包含关系和 Littlewood-Paley 特征
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-16 DOI: 10.1007/s11118-024-10136-6
Dominic Breit, Andrea Cianchi
{"title":"Inclusion Relations Among Fractional Orlicz-Sobolev Spaces and a Littlewood-Paley Characterization","authors":"Dominic Breit, Andrea Cianchi","doi":"10.1007/s11118-024-10136-6","DOIUrl":"https://doi.org/10.1007/s11118-024-10136-6","url":null,"abstract":"<p>Embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. In particular, besides recovering standard embeddings for classical fractional Sobolev spaces, novel results are derived in borderline situations where the latter fail. For instance, limiting embeddings of Pohozhaev-Trudinger-Yudovich type into exponential spaces are offered. The equivalence of Gagliardo-Slobodeckij norms in fractional Orlicz-Sobolev spaces to norms defined via Littlewood-Paley decompositions, oscillations, or Besov type difference quotients is established as well. This equivalence, of independent interest, is a key tool in the proof of the relevant embeddings. They also rest upon a new optimal inequality for convolutions in Orlicz spaces.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"42 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566728","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
Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise 受随机噪声强迫的三维磁流体力学系统定律中的非唯一性
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-13 DOI: 10.1007/s11118-024-10128-6
Kazuo Yamazaki
{"title":"Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise","authors":"Kazuo Yamazaki","doi":"10.1007/s11118-024-10128-6","DOIUrl":"https://doi.org/10.1007/s11118-024-10128-6","url":null,"abstract":"<p>We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system that is forced by random noise of an additive and a linear multiplicative type and has viscous and magnetic diffusion, both of which are weaker than a full Laplacian. We apply convex integration to both equations of velocity and magnetic fields in order to obtain the non-uniqueness in law in the class of probabilistically strong solutions.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566951","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 Bakry-Émery Approach to Lipschitz Transportation on Manifolds 积分榜上的 Lipschitz Transportation 的 Bakry-Émery 方法
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-11 DOI: 10.1007/s11118-024-10138-4
Pablo López-Rivera
{"title":"A Bakry-Émery Approach to Lipschitz Transportation on Manifolds","authors":"Pablo López-Rivera","doi":"10.1007/s11118-024-10138-4","DOIUrl":"https://doi.org/10.1007/s11118-024-10138-4","url":null,"abstract":"<p>On weighted Riemannian manifolds we prove the existence of globally Lipschitz transport maps between the weight (probability) measure and log-Lipschitz perturbations of it, via Kim and Milman’s diffusion transport map, assuming that the curvature-dimension condition <span>(varvec{textrm{CD}(rho _{1}, infty )})</span> holds, as well as a second order version of it, namely <span>(varvec{Gamma _{3} ge rho _{2} Gamma _{2}})</span>. We get new results as corollaries to this result, as the preservation of Poincaré’s inequality for the exponential measure on <span>(varvec{(0,+infty )})</span> when perturbed by a log-Lipschitz potential and a new growth estimate for the Monge map pushing forward the gamma distribution on <span>(varvec{(0,+infty )})</span> (then getting as a particular case the exponential one), via Laguerre’s generator.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"440 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603154","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
Obstacle Problems with Double Boundary Condition for Least Gradient Functions in Metric Measure Spaces 公度量空间中最小梯度函数的双边界条件障碍问题
IF 1.1 3区 数学
Potential Analysis Pub Date : 2024-04-03 DOI: 10.1007/s11118-024-10135-7
Josh Kline
{"title":"Obstacle Problems with Double Boundary Condition for Least Gradient Functions in Metric Measure Spaces","authors":"Josh Kline","doi":"10.1007/s11118-024-10135-7","DOIUrl":"https://doi.org/10.1007/s11118-024-10135-7","url":null,"abstract":"<p>In the setting of a metric space equipped with a doubling measure supporting a (1, 1)-Poincaré inequality, we study the problem of minimizing the BV-energy in a bounded domain <span>(Omega )</span> of functions bounded between two obstacle functions inside <span>(Omega )</span>, and whose trace lies between two prescribed functions on the boundary. If the class of candidate functions is nonempty, we show that solutions exist for continuous obstacles and continuous boundary data when <span>(Omega )</span> is a uniform domain whose boundary is of positive mean curvature in the sense of Lahti, Malý, Shanmugalingam, and Speight (2019). While such solutions are not unique in general, we show the existence of unique minimal solutions. Since candidate functions need not agree outside of the domain, standard compactness arguments fail to provide existence of weak solutions as they are defined for the problem with single boundary condition. To overcome this, we introduce a class of <span>( varepsilon )</span>-<i>weak solutions</i> as an intermediate step. Our existence results generalize those of Ziemer and Zumbrun (1999), who studied this problem in the Euclidean setting with a single obstacle and single boundary condition.</p>","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566749","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
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