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Zeitschrift fur Analysis und ihre Anwendungen最新文献

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Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p to p^*(p,n)$ 不规则域的Sobolev嵌入定理及p 到p^*(p,n)$的不连续
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2016-01-01 DOI: 10.4171/ZAA/1558
T. Roskovec
{"title":"Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p to p^*(p,n)$","authors":"T. Roskovec","doi":"10.4171/ZAA/1558","DOIUrl":"https://doi.org/10.4171/ZAA/1558","url":null,"abstract":"There are a lot of results on the field of characterization of qΩ(p) for classes of domains. For a Lipschitz domain Ω the function p∗(p) = qΩ(p) is continuous and even smooth, (see (1.1)), this was proven by Sobolev in 1938 [12]. Later, the embedding was examined on some more problematic classes of domains by V. G. Maz’ya [9, 10], O. V. Besov and V. P. Il’in [3], T. Kilpelainen and J. Malý [5], D. A. Labutin [6, 7], B. V. Trushin [13, 14] and others. For further results and motivation we recommend the introduction by O. V. Besov [2]. Even considering somehow irregular domains, examined classes of domains have always qΩ(p) somehow nice and continuous. We construct a domain Ω such that the function of the optimal embedding qΩ(p) is continuous up to some point, has a leap at this point and then it is continuous again. The point of discontinuity p0 ∈ [n,∞) and the size of the leap can be chosen as desired. Our work is inspired by the construction of a domain in [4], but our proof is completely different. The original article shows the construction of such a domain","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83445784","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
Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane 平面上微分系统的共振Sturm-Liouville边值问题
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2016-01-01 DOI: 10.4171/ZAA/1554
A. Boscaggin, M. Garrione
{"title":"Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane","authors":"A. Boscaggin, M. Garrione","doi":"10.4171/ZAA/1554","DOIUrl":"https://doi.org/10.4171/ZAA/1554","url":null,"abstract":"We study the Sturm-Liouville boundary value problem associated with the planar differential system Jz′ = ∇V (z) + R(t, z), where V (z) is positive and positively 2-homogeneous and R(t, z) is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed. MSC 2010 Classification 34B15.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81763502","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: 2
Which Functions are Fractionally Differentiable 哪些函数是分数可微的
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2016-01-01 DOI: 10.4171/ZAA/1574
G. Vainikko
{"title":"Which Functions are Fractionally Differentiable","authors":"G. Vainikko","doi":"10.4171/ZAA/1574","DOIUrl":"https://doi.org/10.4171/ZAA/1574","url":null,"abstract":"s of MMA2015, May 26–29, 2015, Sigulda, Latvia c © 2015 WHICH FUNCTIONS ARE FRACTIONALLY DIFFERENTIABLE? G. VAINIKKO Institute of Mathematics, University of Tartu Liivi 2, Tartu 50409, Estonia E-mail: gennadi.vainikko@ut.ee We define a fractional differentiation operator as the inverse to Riemann-Liouville integral operator, and examine the relations of this most natural concept with more popular fractional differentiation operators of Riemann-Liouville and Caputo. Our main result concerns the description of the range of Riemann-Liouville integral operator in the space of continuous functions. As the result we can describe, in particular, the class of functions that are differentiable in the sense of Riemann-Liouville and Caputo. Also the Abel equation with coefficient function of two variables can be examined on the basis of Riemann-Liouville’s operator inversion.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90195021","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: 43
Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions 线性运动硬化准静态塑性的最优控制III:最优性条件
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2016-01-01 DOI: 10.4171/ZAA/1556
G. Wachsmuth
{"title":"Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions","authors":"G. Wachsmuth","doi":"10.4171/ZAA/1556","DOIUrl":"https://doi.org/10.4171/ZAA/1556","url":null,"abstract":"In this paper we consider an optimal control problem governed by a rate-independent variational inequality arising in quasistatic plasticity with linear kinematic hardening. Since the solution operator of a variational inequality is not differentiable, the KKT system is not a necessary optimality condition. We show a system of weakly stationary type by passing to the limit with the optimality system of a regularized and time-discretized problem.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81104327","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: 24
Asymptotic Almost Periodicity to Some Evolution Equations 一类演化方程的渐近概周期性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1549
Rongnian Wang, Qiaomin Xiang, Yong Zhou
{"title":"Asymptotic Almost Periodicity to Some Evolution Equations","authors":"Rongnian Wang, Qiaomin Xiang, Yong Zhou","doi":"10.4171/ZAA/1549","DOIUrl":"https://doi.org/10.4171/ZAA/1549","url":null,"abstract":"In this paper, we introduce a new notion of semi-Lipschitz continuity for the class of asymptotically almost periodic functions and establish new existence theorems for asymptotically almost periodic mild solutions to some semilinear abstract evolution equations upon making some suitable assumptions. As one would expect, the results presented here would generalize and improve some recent results in this area.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90934063","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
Radon–Nikodým Theorems for Finitely Additive Multimeasures Radon-Nikodým有限可加多测度定理
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1545
L. Piazza, G. Porcello
{"title":"Radon–Nikodým Theorems for Finitely Additive Multimeasures","authors":"L. Piazza, G. Porcello","doi":"10.4171/ZAA/1545","DOIUrl":"https://doi.org/10.4171/ZAA/1545","url":null,"abstract":". In this paper we deal with interval multimeasures. We show some Radon-Nikod´ym theorems for such multimeasures using multival- ued Henstock or Henstock-Kurzweil-Pettis derivatives. We do not use the separability assumption in the results.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77857896","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: 10
Existence of a positive solution to Kirchhoff problems involving the fractional Laplacian 涉及分数阶拉普拉斯的Kirchhoff问题正解的存在性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1547
B. Ge, Chao Zhang
{"title":"Existence of a positive solution to Kirchhoff problems involving the fractional Laplacian","authors":"B. Ge, Chao Zhang","doi":"10.4171/ZAA/1547","DOIUrl":"https://doi.org/10.4171/ZAA/1547","url":null,"abstract":"The goal of this paper is to establish the existence of a positive solution to the following fractional Kirchhoff-type problem ( 1 + λ ∫ RN (∣∣(−∆)α2 u(x)∣∣2 + V (x)u2) dx)[(−∆)αu+ V (x)u] = f(u) in R , where N ≥ 2, λ ≥ 0 is a parameter, α ∈ (0, 1), (−∆)α stands for the fractional Laplacian, f ∈ C(R+,R+). Using a variational method combined with suitable truncation techniques, we obtain the existence of at least one positive solution without compactness conditions.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77691982","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: 6
Positive Solutions for Nonlinear Nonhomogeneous Robin Problems 非线性非齐次Robin问题的正解
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1548
L. Gasiński, D. O’Regan, Nikolaos S. Papageorgiou
{"title":"Positive Solutions for Nonlinear Nonhomogeneous Robin Problems","authors":"L. Gasiński, D. O’Regan, Nikolaos S. Papageorgiou","doi":"10.4171/ZAA/1548","DOIUrl":"https://doi.org/10.4171/ZAA/1548","url":null,"abstract":"We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near 0+ and near +∞. We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88416065","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: 10
Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences 渐近概周期序列离散半群与空间的一致指数稳定性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1550
Nisar Ahmad, Habiba Khalid, A. Zada
{"title":"Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences","authors":"Nisar Ahmad, Habiba Khalid, A. Zada","doi":"10.4171/ZAA/1550","DOIUrl":"https://doi.org/10.4171/ZAA/1550","url":null,"abstract":"We prove that the discrete semigroup T = {T (n) : n ∈ Z+} is uniformly exponentially stable if and only if for each z(n) ∈ AAP0(Z+,X ) the solution of the Cauchy problem { yn+1 = T (1)yn + z(n + 1), y(0) = 0 belongs to AAP0(Z+,X ). Where T (1) is the algebraic generator of T, Z+ is the set of all non-negative integers and X is a complex Banach space. Our proof uses the approach of discrete evolution semigroups.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81471010","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: 4
Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability 线性运动硬化拟静态塑性的最优控制II:正则化与可微性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI: 10.4171/ZAA/1546
G. Wachsmuth
{"title":"Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening II: Regularization and Differentiability","authors":"G. Wachsmuth","doi":"10.4171/ZAA/1546","DOIUrl":"https://doi.org/10.4171/ZAA/1546","url":null,"abstract":"We consider an optimal control problem governed by an evolution variational inequality arising in quasistatic plasticity with linear kinematic hardening. A regularization of the time-discrete problem is derived. The regularized forward problem can be interpreted as system of coupled quasilinear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear system. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86786067","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: 23
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