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p-Laplacian problem in a Riemannian manifold
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-26 DOI: 10.1007/s13324-025-01031-3
J. Vanterler da C. Sousa, Lamine Mbarki, Leandro S. Tavares
{"title":"p-Laplacian problem in a Riemannian manifold","authors":"J. Vanterler da C. Sousa,&nbsp;Lamine Mbarki,&nbsp;Leandro S. Tavares","doi":"10.1007/s13324-025-01031-3","DOIUrl":"10.1007/s13324-025-01031-3","url":null,"abstract":"<div><p>This paper is divided into two parts. First, we will prove the existence of solutions of the <i>p</i>-Laplacian equation in the Riemannian manifold in the space <span>({mathcal {H}}^{alpha ,p}_{loc}({mathcal {N}}))</span>. On the other hand, we will give a criterion to obtain a positive lower bound for <span>(lambda _{1,p}(Omega ))</span>, where is a bounded domain <span>(Omega subset {mathcal {N}})</span>. In the first result, we do not consider a bounded subset on the Riemannian manifold <span>({mathcal {N}})</span>. \u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143496825","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
Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1007/s13324-025-01030-4
Bingxiao Liu, Dominik Zielinski
{"title":"Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros","authors":"Bingxiao Liu,&nbsp;Dominik Zielinski","doi":"10.1007/s13324-025-01030-4","DOIUrl":"10.1007/s13324-025-01030-4","url":null,"abstract":"<div><p>We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01030-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homogenization of convolution type semigroups in high contrast media
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-21 DOI: 10.1007/s13324-025-01034-0
Andrey Piatnitski, Elena Zhizhina
{"title":"Homogenization of convolution type semigroups in high contrast media","authors":"Andrey Piatnitski,&nbsp;Elena Zhizhina","doi":"10.1007/s13324-025-01034-0","DOIUrl":"10.1007/s13324-025-01034-0","url":null,"abstract":"<div><p>The paper deals with the asymptotic properties of semigroups associated with Markov jump processes in a high contrast periodic medium in <span>(mathbb {R}^d)</span>, <span>(dge 1)</span>. In order to study the limit behaviour of these semigroups we equip the corresponding Markov processes with an extra variable that characterizes the position of the process inside the period, and show that the limit dynamics of these two-component processes remains Markov. We describe the limit process and prove the convergence of the corresponding semigroups as well as the convergence in law of the extended processes in the path space. Since the components of the limit process are coupled, the dynamics of the first (spacial) component need not have a semigroup property. We derive the evolution equation with a memory term for the dynamics of this component of the limit process. We also discuss the construction of the limit semigroup in the <span>(L^2)</span> space and study the spectrum of its generator.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01034-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retraction Note: Normal functions and products of spherical derivatives
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-21 DOI: 10.1007/s13324-025-01040-2
Yan Xu, Huiling Qiu
{"title":"Retraction Note: Normal functions and products of spherical derivatives","authors":"Yan Xu,&nbsp;Huiling Qiu","doi":"10.1007/s13324-025-01040-2","DOIUrl":"10.1007/s13324-025-01040-2","url":null,"abstract":"","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465970","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
Blow-up of solutions to fractional quasilinear hyperbolic problem
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s13324-025-01033-1
J. Vanterler da C. Sousa, D. S. Oliveira
{"title":"Blow-up of solutions to fractional quasilinear hyperbolic problem","authors":"J. Vanterler da C. Sousa,&nbsp;D. S. Oliveira","doi":"10.1007/s13324-025-01033-1","DOIUrl":"10.1007/s13324-025-01033-1","url":null,"abstract":"<div><p>In this paper, we consider blow-up solutions of a nonlinear hyperbolic fractional equation with variable exponents of nonlinearities in the fractional space <span>(mathcal {H}_{p(xi )}^{alpha }(Omega ))</span>. To achieve this, we introduce a control function and use energy inequalities to discuss various estimates. In this sense, we address the problem of non-existence of solutions and derive an estimate for the upper bound of the blow-up time. Finally, we provide classical theoretical insights into possible special cases of the results obtained in this study.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01033-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolation of variable Hardy–Lorentz–Karamata spaces associated with rearrangement functions
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-20 DOI: 10.1007/s13324-025-01032-2
Zhiwei Hao, Libo Li, Ferenc Weisz
{"title":"Interpolation of variable Hardy–Lorentz–Karamata spaces associated with rearrangement functions","authors":"Zhiwei Hao,&nbsp;Libo Li,&nbsp;Ferenc Weisz","doi":"10.1007/s13324-025-01032-2","DOIUrl":"10.1007/s13324-025-01032-2","url":null,"abstract":"<div><p>In this article, we introduce variable Lorentz–Karamata spaces <span>({mathcal {L}}_{p(cdot ),q,b}(R))</span> defined by rearrangement functions and develop the martingale theory in this framework. The real interpolation theory for variable Lorentz–Karamata spaces is presented. Based on this and the new atomic decomposition, we study the real interpolation theory for variable martingale Hardy–Lorentz–Karamata spaces. We also characterize the real interpolation spaces between variable martingale Hardy spaces and <span>(BMO_2)</span> spaces. The results obtained here generalize the previous results for variable Lorentz spaces as well as for variable martingale Hardy–Lorentz spaces. Moreover, we remove the condition <span>(theta +p_-&gt;1)</span> in [Banach J. Math. Anal. 2023, 17(3): 47].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01032-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-13 DOI: 10.1007/s13324-025-01029-x
Ying Yang, Haiyan Jin, Guangsheng Wei
{"title":"Inverse scattering problems for the Dirac operator on the line with partial knowledge of the potential","authors":"Ying Yang,&nbsp;Haiyan Jin,&nbsp;Guangsheng Wei","doi":"10.1007/s13324-025-01029-x","DOIUrl":"10.1007/s13324-025-01029-x","url":null,"abstract":"<div><p>The inverse scattering problem for the Dirac equation on the real line are considered. It is shown that the potential on the real line is uniquely determined in terms of the mixed scattering data which consists of the knowledge of the potential on the right (left) half line of the real axis and the reflection coefficient from the right (left). In particular, neither the bound states or the bound state norming constants are needed. The method is based on a factorization of a scattering matrix.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396479","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
Normality concerning the sequence of multiple functions
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-10 DOI: 10.1007/s13324-025-01024-2
Dongmei Wei, Fei Li, Yan Xu
{"title":"Normality concerning the sequence of multiple functions","authors":"Dongmei Wei,&nbsp;Fei Li,&nbsp;Yan Xu","doi":"10.1007/s13324-025-01024-2","DOIUrl":"10.1007/s13324-025-01024-2","url":null,"abstract":"<div><p>Let <span>({f_n})</span> be a sequence of meromorphic functions defined in a domain <i>D</i>, and let <span>({psi _n})</span> be a sequence of holomorphic functions on <i>D</i>, whose zeros are multiple, such that <span>(psi _nrightarrow psi )</span> converges locally uniformly in <i>D</i>, where <span>(psi (not equiv 0))</span> is holomorphic in <i>D</i>. If, (1) <span>(f_nne 0)</span> and <span>(f_n^{(k)}ne 0)</span>; (2) all zeros of <span>(f_n^{(k)}-psi _n)</span> have multiplicities at least <span>((k+2)/k)</span>, then <span>({f_n})</span> is normal in <i>D</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373342","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
Pointwise approximation on the Alice Roth’s Swiss cheese
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1007/s13324-025-01026-0
Eduardo S. Zeron, Jesús Emmanuel Castillo
{"title":"Pointwise approximation on the Alice Roth’s Swiss cheese","authors":"Eduardo S. Zeron,&nbsp;Jesús Emmanuel Castillo","doi":"10.1007/s13324-025-01026-0","DOIUrl":"10.1007/s13324-025-01026-0","url":null,"abstract":"<div><p>We show that the complex conjugate function <span>(zmapsto overline{z})</span> cannot be <i>pointwise</i> approximated by holomorphic polynomials on the Alice Roth’s Swiss cheese <span>(Q_Rsubset mathbb {C})</span>. Moreover, under some extra hypotheses, we also show that the complex conjugate cannot be <i>pointwise</i> approximated either by functions holomorphic on <span>(Q_R)</span>.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01026-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of normalized solutions to a class of non-autonomous (p, q)-Laplacian equations
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-02-08 DOI: 10.1007/s13324-025-01025-1
Xiaoxiao Cui, Anran Li, Chongqing Wei
{"title":"Existence of normalized solutions to a class of non-autonomous (p, q)-Laplacian equations","authors":"Xiaoxiao Cui,&nbsp;Anran Li,&nbsp;Chongqing Wei","doi":"10.1007/s13324-025-01025-1","DOIUrl":"10.1007/s13324-025-01025-1","url":null,"abstract":"<div><p>We study the multiplicity of normalized solutions of the following (<i>p</i>, <i>q</i>)-Laplacian equation </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} -Delta _p u-Delta _q u=lambda |u|^{p-2}u+V(epsilon x)f(u) text {in} mathbb {R}^N, int _{mathbb {R}^N}|u|^pdx=a^p, end{array}right. end{aligned}$$</span></div></div><p>where <span>(1&lt;p&lt;q&lt;N)</span>, <i>a</i>, <span>(epsilon &gt;0)</span>, <span>(Delta _lu:=hbox {div}(|nabla u|^{l-2}nabla u))</span> with <span>(lin {p,q})</span>, stands for the <i>l</i>-Laplacian operator. <span>(lambda in mathbb {R})</span> is an unknown parameter that appears as a Lagrange multiplier. <span>(V:mathbb {R}^Nrightarrow mathbb {R})</span> is a continuous function with some proper assumptions. <i>f</i> is a continuous function with <span>(L^p)</span>-mass subcritical growth. By using variational methods, we prove that the equation has multiple normalized solutions, as <span>(epsilon )</span> is small enough. Precisely, the number of normalized solutions is at least twice that of the global maximum points of <i>V</i>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361847","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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