The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order

[2105.13612] The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2105.13612 (math) [Submitted on 28 May 2021 ( v1 ), last revised 14 Jul 2021 (this version, v2)] Title: The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order Authors: Jamil Chaker , Minhyun Kim , Marvin Weidner View PDF HTML (experimental) Abstract: In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrability and different orders of differentiability. Our method is based on the concentration-compactness principle which we extend to this class of operators. One consequence of our main result is the existence of a nontrivial nonnegative solution to the corresponding critical problem. Comments: 19 pages Subjects: Analysis of PDEs (math.AP) MSC classes: 35R11, 35A01, 49J35, 46E35, 46B50 Cite as: arXiv:2105.13612 [math.AP] (or arXiv:2105.13612v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2105.13612 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nonlinear Anal. 232 (2023), Paper No. 113254, 18 pp Related DOI : https://doi.org/10.1016/j.na.2023.113254 Focus to learn more DOI(s) linking to related resources Submission history From: Minhyun Kim [ view email ] [v1] Fri, 28 May 2021 06:45:03 UTC (17 KB) [v2] Wed, 14 Jul 2021 15:53:40 UTC (18 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2021-05 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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