Pub Date : 2023-01-13DOI: 10.1007/s13163-022-00454-x
P. Pedregal
{"title":"On a special class of non-local variational problems","authors":"P. Pedregal","doi":"10.1007/s13163-022-00454-x","DOIUrl":"https://doi.org/10.1007/s13163-022-00454-x","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"1 1","pages":"1-15"},"PeriodicalIF":0.8,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47268567","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}
Pub Date : 2023-01-04DOI: 10.1007/s13163-022-00451-0
Shuai Yao, Haibo Chen
{"title":"Multiple normalized solutions for the coupled Hartree–Fock system with upper critical exponent","authors":"Shuai Yao, Haibo Chen","doi":"10.1007/s13163-022-00451-0","DOIUrl":"https://doi.org/10.1007/s13163-022-00451-0","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"1 1","pages":"1-46"},"PeriodicalIF":0.8,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45373465","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}
Pub Date : 2023-01-01Epub Date: 2022-10-10DOI: 10.1007/s13163-022-00444-z
Balázs Csikós, Amr Elnashar, Márton Horváth
Csikós and Horváth proved in J Geom Anal 28(4): 3458-3476, (2018) that if a connected Riemannian manifold of dimension at least 4 is harmonic, then the total scalar curvatures of tubes of small radius about an arbitrary regular curve depend only on the length of the curve and the radius of the tube, and conversely, if the latter condition holds for cylinders, i.e., for tubes about geodesic segments, then the manifold is harmonic. In the present paper, we show that in contrast to the higher dimensional case, a connected 3-dimensional Riemannian manifold has the above mentioned property of tubes if and only if the manifold is a D'Atri space, furthermore, if the space has bounded sectional curvature, then it is enough to require the total scalar curvature condition just for cylinders to imply that the space is D'Atri. This result gives a negative answer to a question posed by Gheysens and Vanhecke. To prove these statements, we give a characterization of D'Atri spaces in terms of the total scalar curvature of geodesic hemispheres in any dimension.
{"title":"D'Atri spaces and the total scalar curvature of hemispheres, tubes and cylinders.","authors":"Balázs Csikós, Amr Elnashar, Márton Horváth","doi":"10.1007/s13163-022-00444-z","DOIUrl":"10.1007/s13163-022-00444-z","url":null,"abstract":"<p><p>Csikós and Horváth proved in J Geom Anal 28(4): 3458-3476, (2018) that if a connected Riemannian manifold of dimension at least 4 is harmonic, then the total scalar curvatures of tubes of small radius about an arbitrary regular curve depend only on the length of the curve and the radius of the tube, and conversely, if the latter condition holds for cylinders, i.e., for tubes about <i>geodesic</i> segments, then the manifold is harmonic. In the present paper, we show that in contrast to the higher dimensional case, a connected 3-dimensional Riemannian manifold has the above mentioned property of tubes if and only if the manifold is a D'Atri space, furthermore, if the space has bounded sectional curvature, then it is enough to require the total scalar curvature condition just for cylinders to imply that the space is D'Atri. This result gives a negative answer to a question posed by Gheysens and Vanhecke. To prove these statements, we give a characterization of D'Atri spaces in terms of the total scalar curvature of geodesic hemispheres in any dimension.</p>","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"36 3","pages":"887-898"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10471713/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10202625","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}
Pub Date : 2023-01-01Epub Date: 2022-06-20DOI: 10.1007/s13163-022-00429-y
Giovanni E Comi, Giorgio Stefani
We continue the study of the space of functions with bounded fractional variation in of order introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373-3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic behavior of the fractional operators involved as . We prove that the -gradient of a -function converges in to the gradient for all as . Moreover, we prove that the fractional -variation converges to the standard De Giorgi's variation both pointwise and in the -limit sense as . Finally, we prove that the fractional -variation converges to the fractional -variation both pointwise and in the -limit sense as for any given .
我们继续研究我们之前的工作 (Comi and Stefani in J Funct Anal 277(10):3373-3435, 2019) 中引入的 R n 中阶 α∈ ( 0 , 1 ) 的有界分数变化函数空间 B V α ( R n ) 。在对 Comi 和 Stefani (2019) 的某些结果做了一些技术上的改进之后（这些结果可能会引起一些单独的兴趣），我们讨论了所涉及的分数算子在 α → 1 - 时的渐近行为。我们证明，当 α → 1 - 时，W 1 , p 函数的 α 梯度在 L p 中收敛于所有 p∈ [ 1 , + ∞ ) 的梯度。此外，我们证明当 α → 1 - 时，分数 α 变量在点上和Γ - 极限意义上都收敛于标准的 De Giorgi 变量。最后，我们证明，对于任何给定的 α∈ ( 0 , 1 ) ，分式 β 变量在 β → α - 时都会在点上和 Γ - 极限意义上收敛于分式 α 变量。
{"title":"A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I.","authors":"Giovanni E Comi, Giorgio Stefani","doi":"10.1007/s13163-022-00429-y","DOIUrl":"10.1007/s13163-022-00429-y","url":null,"abstract":"<p><p>We continue the study of the space <math><mrow><mi>B</mi> <msup><mi>V</mi> <mi>α</mi></msup> <mrow><mo>(</mo> <msup><mrow><mi>R</mi></mrow> <mi>n</mi></msup> <mo>)</mo></mrow> </mrow> </math> of functions with bounded fractional variation in <math> <msup><mrow><mi>R</mi></mrow> <mi>n</mi></msup> </math> of order <math><mrow><mi>α</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></mrow> </math> introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373-3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic behavior of the fractional operators involved as <math><mrow><mi>α</mi> <mo>→</mo> <msup><mn>1</mn> <mo>-</mo></msup> </mrow> </math> . We prove that the <math><mi>α</mi></math> -gradient of a <math><msup><mi>W</mi> <mrow><mn>1</mn> <mo>,</mo> <mi>p</mi></mrow> </msup> </math> -function converges in <math><msup><mi>L</mi> <mi>p</mi></msup> </math> to the gradient for all <math><mrow><mi>p</mi> <mo>∈</mo> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mo>+</mo> <mi>∞</mi> <mo>)</mo></mrow> </math> as <math><mrow><mi>α</mi> <mo>→</mo> <msup><mn>1</mn> <mo>-</mo></msup> </mrow> </math> . Moreover, we prove that the fractional <math><mi>α</mi></math> -variation converges to the standard De Giorgi's variation both pointwise and in the <math><mi>Γ</mi></math> -limit sense as <math><mrow><mi>α</mi> <mo>→</mo> <msup><mn>1</mn> <mo>-</mo></msup> </mrow> </math> . Finally, we prove that the fractional <math><mi>β</mi></math> -variation converges to the fractional <math><mi>α</mi></math> -variation both pointwise and in the <math><mi>Γ</mi></math> -limit sense as <math><mrow><mi>β</mi> <mo>→</mo> <msup><mi>α</mi> <mo>-</mo></msup> </mrow> </math> for any given <math><mrow><mi>α</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></mrow> </math> .</p>","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"36 2","pages":"491-569"},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10147820/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9410531","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}
Pub Date : 2023-01-01DOI: 10.1007/s13163-021-00417-8
Diego Alonso-Orán, Fernando Chamizo, Ángel D Martínez, Albert Mas
In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.
{"title":"Pointwise monotonicity of heat kernels.","authors":"Diego Alonso-Orán, Fernando Chamizo, Ángel D Martínez, Albert Mas","doi":"10.1007/s13163-021-00417-8","DOIUrl":"https://doi.org/10.1007/s13163-021-00417-8","url":null,"abstract":"<p><p>In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.</p>","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"36 1","pages":"207-220"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9852120/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9166787","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}
Pub Date : 2022-11-25DOI: 10.1007/s13163-023-00478-x
A. Dom'inguez, L. N. Macarro
{"title":"On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities","authors":"A. Dom'inguez, L. N. Macarro","doi":"10.1007/s13163-023-00478-x","DOIUrl":"https://doi.org/10.1007/s13163-023-00478-x","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48645881","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}
Pub Date : 2022-11-16DOI: 10.1007/s13163-022-00446-x
F. Corrêa, Gelson C. G. dos Santos, L. S. Tavares
{"title":"Existence and multiplicity of solutions for a singular anisotropic problem with a sign-changing term","authors":"F. Corrêa, Gelson C. G. dos Santos, L. S. Tavares","doi":"10.1007/s13163-022-00446-x","DOIUrl":"https://doi.org/10.1007/s13163-022-00446-x","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47584036","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}
Pub Date : 2022-10-09DOI: 10.1007/s13163-022-00443-0
Phuong Le
{"title":"Liouville theorem for Hénon-Hardy systems in the unit ball","authors":"Phuong Le","doi":"10.1007/s13163-022-00443-0","DOIUrl":"https://doi.org/10.1007/s13163-022-00443-0","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"36 1","pages":"827 - 840"},"PeriodicalIF":0.8,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49318727","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}
Pub Date : 2022-09-23DOI: 10.1007/s13163-022-00442-1
Victor J. W. Guo
{"title":"Some q-supercongruences from the Gasper and Rahman quadratic summation","authors":"Victor J. W. Guo","doi":"10.1007/s13163-022-00442-1","DOIUrl":"https://doi.org/10.1007/s13163-022-00442-1","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"36 1","pages":"993 - 1002"},"PeriodicalIF":0.8,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43767831","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}
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