Singular set estimates for solutions to elliptic equations in higher co-dimension

[2502.03294] Singular set estimates for solutions to elliptic equations in higher co-dimension Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2502.03294 (math) [Submitted on 5 Feb 2025 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Singular set estimates for solutions to elliptic equations in higher co-dimension Authors: Max Engelstein , Cole Jeznach , Yannick Sire View a PDF of the paper titled Singular set estimates for solutions to elliptic equations in higher co-dimension, by Max Engelstein and 2 other authors View PDF HTML (experimental) Abstract: Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good understanding of the vanishing order and size of singular and zero set of solutions. Such estimates also hold at the boundary, provided that the domain is sufficiently regular. In this work, we investigate the boundary behavior of solutions to a class of elliptic equations in the higher co-dimension setting, whose coefficients are neither uniformly elliptic, nor uniformly Lipschitz. Despite these challenges, we are still able to show analogous estimates on the singular set of such solutions near the boundary. Our main technical advance is a variant of the Cheeger-Naber-Valtorta quantitative stratification scheme using cones instead of planes. Comments: 85 pages, 1 figure. Minor changes made to previous version Subjects: Analysis of PDEs (math.AP) MSC classes: 35J70, 28A78, 35A02 Cite as: arXiv:2502.03294 [math.AP] (or arXiv:2502.03294v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2502.03294 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Cole Jeznach [ view email ] [v1] Wed, 5 Feb 2025 15:52:40 UTC (86 KB) [v2] Tue, 14 Apr 2026 08:55:56 UTC (80 KB) Full-text links: Access Paper: View a PDF of the paper titled Singular set estimates for solutions to elliptic equations in higher co-dimension, by Max Engelstein and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2025-02 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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

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