Regularity for nonlocal problems with non-standard growth

[2111.09182] Regularity for nonlocal problems with non-standard growth Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2111.09182 (math) [Submitted on 17 Nov 2021] Title: Regularity for nonlocal problems with non-standard growth Authors: Jamil Chaker , Minhyun Kim , Marvin Weidner View PDF HTML (experimental) Abstract: We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of $(p,q)$-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness and Hölder continuity of minimizers and weak solutions. Our approach is based on the study of corresponding De Giorgi classes. Comments: 30 pages Subjects: Analysis of PDEs (math.AP) MSC classes: 35B65, 47G20, 35D30, 35B45, 35A15 Cite as: arXiv:2111.09182 [math.AP] (or arXiv:2111.09182v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2111.09182 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Calc. Var. Partial Differential Equations 61 (2022), no. 6, Paper No. 227, 31 pp Related DOI : https://doi.org/10.1007/s00526-022-02364-8 Focus to learn more DOI(s) linking to related resources Submission history From: Minhyun Kim [ view email ] [v1] Wed, 17 Nov 2021 15:19:41 UTC (26 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2021-11 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Regularity for nonlocal problems with non-standard growth#677291
• Removable singularities for nonlocal minimal graphs#677351
• Removable singularities for nonlocal minimal graphs#674154
• Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon#1062760
• Semiclassical Liouville Theory on the Real Projective Plane: A Complex Interpretation of the Bootstrap#1141636