Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature

[2101.06903] Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2101.06903 (math) [Submitted on 18 Jan 2021] Title: Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature Authors: Jongmyeong Kim , Minhyun Kim , Ki-Ahm Lee View PDF HTML (experimental) Abstract: We establish the Krylov Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sectional curvatures. To this end, we first define the nonlocal Pucci operators on manifolds that give rise to the concept of non-divergence form operators. We then provide the uniform regularity results for these operators which recover the classical results for second order local operators as limits. Subjects: Analysis of PDEs (math.AP) ; Differential Geometry (math.DG) Cite as: arXiv:2101.06903 [math.AP] (or arXiv:2101.06903v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2101.06903 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Calc. Var. Partial Differential Equations 61 (2022), no. 1, Paper No. 22, 29 pp Related DOI : https://doi.org/10.1007/s00526-021-02124-0 Focus to learn more DOI(s) linking to related resources Submission history From: Jongmyeong Kim [ view email ] [v1] Mon, 18 Jan 2021 06:57:00 UTC (24 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2021-01 Change to browse by: math math.DG 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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