Potential Analysis最新文献_第4页

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":"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 (Omega ) of functions bounded between two obstacle functions inside (Omega ), 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 (Omega ) 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 ( varepsilon )-weak solutions 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.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":null,"pages":null},"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

Total Variation Error Bounds for the Approximation of the Invariant Distribution of Parabolic Semilinear SPDEs Using the Standard Euler Scheme 使用标准欧拉方案逼近抛物线半线性 SPDE 的不变分布的总变差误差边界

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-19 DOI: 10.1007/s11118-024-10132-w

Charles-Edouard Bréhier

引用次数: 0

Exponential Contractivity and Propagation of Chaos for Langevin Dynamics of McKean-Vlasov Type with Lévy Noises 带列维噪声的麦金-弗拉索夫型兰万动力学的指数收缩性和混沌传播

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-15 DOI: 10.1007/s11118-024-10130-y

{"title":"Exponential Contractivity and Propagation of Chaos for Langevin Dynamics of McKean-Vlasov Type with Lévy Noises","authors":"","doi":"10.1007/s11118-024-10130-y","DOIUrl":"https://doi.org/10.1007/s11118-024-10130-y","url":null,"abstract":"<h3>Abstract</h3> By the probabilistic coupling approach which combines a new refined basic coupling with the synchronous coupling for Lévy processes, we obtain explicit exponential contraction rates in terms of the standard (L^1) -Wasserstein distance for the following Langevin dynamic ((X_t,Y_t)_{tge 0}) of McKean-Vlasov type on (mathbb R^{2d}) : $$begin{aligned} left{ begin{array}{l} dX_t=Y_t,dt, dY_t=left( b(X_t)+displaystyle int _{mathbb R^d}tilde{b}(X_t,z),mu ^X_t(dz)-{gamma }Y_tright) ,dt+dL_t,quad mu ^X_t=textrm{Law}(X_t), end{array} right. end{aligned}$$ where ({gamma }>0) , (b:mathbb R^drightarrow mathbb R^d) and (tilde{b}:mathbb R^{2d}rightarrow mathbb R^d) are two globally Lipschitz continuous functions, and ((L_t)_{tge 0}) is an (mathbb R^d) -valued pure jump Lévy process. The proof is also based on a novel distance function, which is designed according to the distance of the marginals associated with the constructed coupling process. Furthermore, by applying the coupling technique above with some modifications, we also provide the propagation of chaos uniformly in time for the corresponding mean-field interacting particle systems with Lévy noises in the standard (L^1) -Wasserstein distance as well as with explicit bounds.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155562","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 $$L_{p}-$$ Theory for Integro-Differential Operators with Spatially Dependent Coefficients 关于具有空间依赖系数的积分微分算子的 $$L_{p}-$$ 理论

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-14 DOI: 10.1007/s11118-024-10131-x

Sutawas Janreung, Tatpon Siripraparat, Chukiat Saksurakan

引用次数: 0

Large and Moderate Deviations for Empirical Density Fields of Stochastic Seir Epidemics with Vertex-Dependent Transition Rates 顶点依赖转换率的随机 Seir 流行病经验密度场的大偏差和中偏差

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-09 DOI: 10.1007/s11118-024-10133-9

Xiaofeng Xue, Xueting Yin

引用次数: 0

Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms 相对于非局部迪里希勒形式的弱谐波映射的概率特征

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-09 DOI: 10.1007/s11118-024-10129-5

Fumiya Okazaki

引用次数: 0

Stochastic Generalized Porous Media Equations Over $$sigma $$ -finite Measure Spaces with Non-continuous Diffusivity Function 具有非连续扩散函数的 $$sigma $$ - 无限测度空间上的随机广义多孔介质方程

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-04 DOI: 10.1007/s11118-024-10127-7

Michael Röckner, Weina Wu, Yingchao Xie

{"title":"Stochastic Generalized Porous Media Equations Over $$sigma $$ -finite Measure Spaces with Non-continuous Diffusivity Function","authors":"Michael Röckner, Weina Wu, Yingchao Xie","doi":"10.1007/s11118-024-10127-7","DOIUrl":"https://doi.org/10.1007/s11118-024-10127-7","url":null,"abstract":"In this paper, we prove that stochastic porous media equations over (sigma )-finite measure spaces ((E,mathcal {B},mu )), driven by time-dependent multiplicative noise, with the Laplacian replaced by a self-adjoint transient Dirichlet operator L and the diffusivity function given by a maximal monotone multi-valued function (Psi ) of polynomial growth, have a unique solution. This generalizes previous results in that we work on general measurable state spaces, allow non-continuous monotone functions (Psi ), for which, no further assumptions (as e.g. coercivity) are needed, but only that their multi-valued extensions are maximal monotone and of at most polynomial growth. Furthermore, an (L^p(mu ))-Itô formula in expectation is proved, which is not only crucial for the proof of our main result, but also of independent interest. The result in particular applies to fast diffusion stochastic porous media equations (in particular self-organized criticality models) and cases where E is a manifold or a fractal, and to non-local operators L, as e.g. (L=-f(-Delta )), where f is a Bernstein function.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036020","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

Correction to: Erratum on the labeling of two papers 更正：关于两篇论文标签的勘误

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-28 DOI: 10.1007/s11118-024-10121-z

Potential Analysis Springer

引用次数: 0

A Fourier Integral Formula for Logarithmic Energy 对数能量的傅立叶积分公式

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-09 DOI: 10.1007/s11118-024-10125-9

L. Frerick, J. Müller, T. Thomaser

引用次数: 0

Trace Operator on von Koch’s Snowflake 冯-科赫雪花上的微量运算符

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-09 DOI: 10.1007/s11118-024-10124-w

Krystian Kazaniecki, Michał Wojciechowski

{"title":"Trace Operator on von Koch’s Snowflake","authors":"Krystian Kazaniecki, Michał Wojciechowski","doi":"10.1007/s11118-024-10124-w","DOIUrl":"https://doi.org/10.1007/s11118-024-10124-w","url":null,"abstract":"We study properties of the boundary trace operator on the Sobolev space (W^1_1(Omega )). Using the density result by Koskela and Zhang (Arch. Ration. Mech. Anal. 222(1), 1-14 2016), we define a surjective operator (Tr: W^1_1(Omega _K)rightarrow X(Omega _K)), where (Omega _K) is von Koch’s snowflake and (X(Omega _K)) is a trace space with the quotient norm. Since (Omega _K) is a uniform domain whose boundary is Ahlfors-regular with an exponent strictly bigger than one, it was shown by L. Malý (2017) that there exists a right inverse to Tr, i.e. a linear operator (S: X(Omega _K) rightarrow W^1_1(Omega _K)) such that (Tr circ S= Id_{X(Omega _K)}). In this paper we provide a different, purely combinatorial proof based on geometrical structure of von Koch’s snowflake. Moreover we identify the isomorphism class of the trace space as (ell _1). As an additional consequence of our approach we obtain a simple proof of the Peetre’s theorem (Special Issue 2, 277-282 1979) about non-existence of the right inverse for domain (Omega ) with regular boundary, which explains Banach space geometry cause for this phenomenon.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762459","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