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Zeitschrift fur Analysis und ihre Anwendungen最新文献

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Can one recognize a function from its graph? 我们能从一个函数的图形中认出它吗?
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-30 DOI: 10.4171/zaa/1730
Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka
{"title":"Can one recognize a function from its graph?","authors":"Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka","doi":"10.4171/zaa/1730","DOIUrl":"https://doi.org/10.4171/zaa/1730","url":null,"abstract":"We analyse the “interplay” between analytical properties of a real function on a metric space, on the one hand, and topological properties of its graph, on the other. In particular, we study functions with closed, compact, connected, pathwise connected, or locally connected graphs, and we give nine conditions on the graph which are equivalent to the continuity of a function. A main emphasis is put on examples and counterexamples which illustrate how significant our hypotheses are, and how far sufficient conditions are from being necessary.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136279753","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
Sign changing solutions for critical double phase problems with variable exponent 变指数临界双相问题的变符号解
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-30 DOI: 10.4171/zaa/1731
Nikolaos S. Papageorgiou, Francesca Vetro, Patrick Winkert
{"title":"Sign changing solutions for critical double phase problems with variable exponent","authors":"Nikolaos S. Papageorgiou, Francesca Vetro, Patrick Winkert","doi":"10.4171/zaa/1731","DOIUrl":"https://doi.org/10.4171/zaa/1731","url":null,"abstract":"In this paper, we deal with a double phase problem with variable exponent and a right-hand side consisting of a Carathéodory perturbation defined only locally and of a critical term. We stress that the presence of the critical term inhibits the possibility to apply results of the critical point theory to the corresponding energy functional. Instead, we use suitable cut-off functions and truncation techniques in order to work with a coercive functional. Then, using variational tools and an appropriate auxiliary coercive problem, we can produce a sequence of sign changing solutions to our main problem converging to $0$ in $L^{infty}$ and in the Musielakk–Orlicz Sobolev space.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136279756","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
Global structure of positive solutions for a fourth-order boundary value problem with singular data 一类具有奇异数据的四阶边值问题正解的全局结构
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-30 DOI: 10.4171/zaa/1729
Ruyun Ma, Zhongzi Zhao, Mantang Ma
{"title":"Global structure of positive solutions for a fourth-order boundary value problem with singular data","authors":"Ruyun Ma, Zhongzi Zhao, Mantang Ma","doi":"10.4171/zaa/1729","DOIUrl":"https://doi.org/10.4171/zaa/1729","url":null,"abstract":"We are concerned with a problem described the deformation of a simply supported beam of the form $$ u^{(4)}(x)+c(x)u(x) + sum^p_{i=1}c_idelta(x-x_i)u(x) = lambda a(u(x)) + lambdasum^q_{j=1}a_j(u(x))delta(x-y_j), quad xin (0,1), $$ $$ u(0)=u(1)=u''(0)=u''(1)=0, $$ where $lambda$ is a positive parameter, $cin C([0, 1],mathbb{R})$, $c_i in mathbb{R}$, $a, a_jin C([0,infty),[0,infty))$, $i = 1, 2, ldots, p$, $j= 1, 2, ldots, q$, $p, q in mathbb{N}$. The Dirac delta impulses $delta = delta(x)$ are applied at given points $0 < x_1 < x_2 <cdots < x_p < 1$ and $0 < y_1 < y_2 < cdots < y_q < 1$. We investigate the global structure of positive solutions by the global bifurcation techniques.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136279755","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
Integrability for Hardy operators of double phase 双相Hardy算子的可积性
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-30 DOI: 10.4171/zaa/1732
Yoshihiro Mizuta, Tetsu Shimomura
{"title":"Integrability for Hardy operators of double phase","authors":"Yoshihiro Mizuta, Tetsu Shimomura","doi":"10.4171/zaa/1732","DOIUrl":"https://doi.org/10.4171/zaa/1732","url":null,"abstract":"We establish Hardy–Sobolev and Hardy–Trudinger inequalities in weighted Orlicz spaces on $mathbb{R}^n$. As an application, we prove Hardy–Sobolev and Hardy–Trudinger inequalities in the framework of general double phase functionals given by $$ varphi_p(x,t) = varphi_1(t^p) + varphi_2((b(x)t)^p), quad xin mathbb{R}^n,, t ge 0, $$ where $p>1$, $varphi_1, varphi_2$ are positive convex functions on $(0,infty)$ and $b$ is a non-negative function on $[0,infty)$ which is Hölder continuous of order $theta in (0,1]$.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136279750","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
Cocompact embedding theorem for functions of bounded variation into Lorentz spaces 有界变分函数在洛伦兹空间中的紧嵌入定理
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-13 DOI: 10.4171/zaa/1728
Lin Zhao
{"title":"Cocompact embedding theorem for functions of bounded variation into Lorentz spaces","authors":"Lin Zhao","doi":"10.4171/zaa/1728","DOIUrl":"https://doi.org/10.4171/zaa/1728","url":null,"abstract":"We show that the embedding $dot{mathrm{BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,q}(mathbb{R}^N)$, $q>1$ is cocompact with respect to the group and the profile decomposition for $dot{mathrm{BV}}(mathbb{R}^N)$. This paper extends the cocompactness and profile decomposition for the critical space $L^{1^ast}(mathbb{R}^N)$ to Lorentz spaces $L^{1^ast,q}(mathbb{R}^N)$, $q>1$. A~counterexample for $dot{mathrm{BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,1}(mathbb{R}^N)$ not cocompact is given in the last section.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690095","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
Real interpolations for martingale Hardy–Orlicz–Lorentz spaces 鞅Hardy-Orlicz-Lorentz空间的实插值
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-13 DOI: 10.4171/zaa/1726
Wenfei Fan, Yanmeng Li, Lian Wu
{"title":"Real interpolations for martingale Hardy–Orlicz–Lorentz spaces","authors":"Wenfei Fan, Yanmeng Li, Lian Wu","doi":"10.4171/zaa/1726","DOIUrl":"https://doi.org/10.4171/zaa/1726","url":null,"abstract":"The purpose of this paper is to provide a new proof of real interpolations for martingale Hardy–Orlicz–Lorentz spaces. Different from the usual proof, our approach does not rely on any atomic decompositions. Instead, we establish the result via new Holmstedt’s formulae in martingale Hardy–Orlicz type spaces.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690252","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
Multi-layered tumor cell cultures with almost periodic nutrient supply 多层肿瘤细胞培养，几乎有周期性的营养供应
3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-09-13 DOI: 10.4171/zaa/1727
Homero G. Díaz-Marín
{"title":"Multi-layered tumor cell cultures with almost periodic nutrient supply","authors":"Homero G. Díaz-Marín","doi":"10.4171/zaa/1727","DOIUrl":"https://doi.org/10.4171/zaa/1727","url":null,"abstract":"Modeling of multi-layered cell cultures (MCC) assume flat geometry in a 3D tumor growth model.Some results available in the time-dependent framework assume a periodic nutrient supply $Phi(t)$. Our aim is to generalize such considerations. Namely, we show that a stable oscillating tumor growth arises in the long term, whenever the mean value of the almost periodic nutrient supply $overline{Phi}$ surpasses certain threshold level, $overline{Phi}>tilde{sigma}$. Meanwhile, a vanishing tumor is predicted in the complementary case, $overline{Phi}leq tilde{sigma}$.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135734885","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
Fractional differentiability for elliptic double obstacle problems with measure data 具有测量数据的椭圆型双障碍问题的分数可微性
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-07-10 DOI: 10.4171/zaa/1721
Sun-Sig Byun, Kyeong Song, Yeonghun Youn
{"title":"Fractional differentiability for elliptic double obstacle problems with measure data","authors":"Sun-Sig Byun, Kyeong Song, Yeonghun Youn","doi":"10.4171/zaa/1721","DOIUrl":"https://doi.org/10.4171/zaa/1721","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41740867","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: 1
Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x); q(x))-Laplacian operator 涉及(p(x))的非线性粘弹性板方程解的整体存在性、渐近稳定性和爆破性问(x))拉普拉斯算符
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-06-20 DOI: 10.4171/zaa/1722
M. Shahrouzi, J. Ferreira, F. Tahamtani
{"title":"Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x); q(x))-Laplacian operator","authors":"M. Shahrouzi, J. Ferreira, F. Tahamtani","doi":"10.4171/zaa/1722","DOIUrl":"https://doi.org/10.4171/zaa/1722","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45576763","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: 1
On Korpelevich’s extragradient algorithm 关于Korpelevich的提取算法
IF 1.2 3区 数学
Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2023-06-20 DOI: 10.4171/zaa/1724
Nicholas Pischke
{"title":"On Korpelevich’s extragradient algorithm","authors":"Nicholas Pischke","doi":"10.4171/zaa/1724","DOIUrl":"https://doi.org/10.4171/zaa/1724","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45303874","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
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