SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 224-250, February 2026. Abstract. The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.
{"title":"A Primal-Dual Level Set Method for Computing Geodesic Distances","authors":"Hailiang Liu, Laura Zinnel","doi":"10.1137/24m1721086","DOIUrl":"https://doi.org/10.1137/24m1721086","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 224-250, February 2026. <br/> Abstract. The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"89 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146121993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-06DOI: 10.1016/j.jde.2026.114192
Qi Xiong , Zhenqiu Zhang , Lingwei Ma
In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the regularity criterion.
{"title":"Riesz potential estimates for double obstacle problems with Orlicz growth","authors":"Qi Xiong , Zhenqiu Zhang , Lingwei Ma","doi":"10.1016/j.jde.2026.114192","DOIUrl":"10.1016/j.jde.2026.114192","url":null,"abstract":"<div><div>In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> regularity criterion.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114192"},"PeriodicalIF":2.3,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for self-adjoint operators.
{"title":"On regularity of compressions and diagonals of operator functions","authors":"Vladimir Müller, Yuri Tomilov","doi":"10.1112/jlms.70433","DOIUrl":"https://doi.org/10.1112/jlms.70433","url":null,"abstract":"<p>Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for self-adjoint operators.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-06DOI: 10.1016/j.chaos.2026.118026
Yiqun Yan, Qianwei Zhang, Leiman Fu
{"title":"The role of anxiety in the evolution of cooperative behavior based on spatial interactions","authors":"Yiqun Yan, Qianwei Zhang, Leiman Fu","doi":"10.1016/j.chaos.2026.118026","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118026","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"48 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-06DOI: 10.1016/j.chaos.2026.118041
Anupam Ghosh
{"title":"Ab initio analysis of extreme events in dynamical systems with Rényi entropy production rate","authors":"Anupam Ghosh","doi":"10.1016/j.chaos.2026.118041","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118041","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"31 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-05DOI: 10.1016/j.chaos.2026.118019
Rafael A. Bilbao, Rafael Lucena
{"title":"Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states","authors":"Rafael A. Bilbao, Rafael Lucena","doi":"10.1016/j.chaos.2026.118019","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118019","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"10 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-05DOI: 10.1016/j.amc.2026.129991
Sergio Amat, Sonia Busquier, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez
{"title":"On a weighted Chaikin-type subdivision scheme for non-smooth data","authors":"Sergio Amat, Sonia Busquier, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez","doi":"10.1016/j.amc.2026.129991","DOIUrl":"https://doi.org/10.1016/j.amc.2026.129991","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"89 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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