Local regularity for nonlocal equations with variable exponents

[2107.06043] Local regularity for nonlocal equations with variable exponents Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2107.06043 (math) [Submitted on 13 Jul 2021 ( v1 ), last revised 20 Jul 2021 (this version, v2)] Title: Local regularity for nonlocal equations with variable exponents Authors: Jamil Chaker , Minhyun Kim View PDF HTML (experimental) Abstract: In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrange equations. We show that weak solutions are locally bounded when the variable exponent $p$ is only assumed to be continuous and bounded. Furthermore, we prove that bounded weak solutions are locally Hölder continuous under some additional assumptions on $p$. On the one hand, the class of admissible exponents is assumed to satisfy a log-Hölder-type condition inside the domain, which is essential even in the case of local equations. On the other hand, since we are concerned with nonlocal problems, we need an additional assumption on $p$ outside the domain. Comments: 28 pages, 1 figure. corrected typos, fixed the proof of Theorem 1.5, added two references Subjects: Analysis of PDEs (math.AP) MSC classes: 35B65, 47G20, 35D30, 35B45, 46E35 Cite as: arXiv:2107.06043 [math.AP] (or arXiv:2107.06043v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2107.06043 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Math. Nachr. 296 (2023), no. 9, 4463-4489 Related DOI : https://doi.org/10.1002/mana.202100521 Focus to learn more DOI(s) linking to related resources Submission history From: Minhyun Kim [ view email ] [v1] Tue, 13 Jul 2021 12:53:35 UTC (71 KB) [v2] Tue, 20 Jul 2021 13:08:21 UTC (71 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2021-07 Change to browse by: math References & Citations SciX 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)

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