Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type

[2601.07140] Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2601.07140 (math) [Submitted on 12 Jan 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type Authors: Carlo Alberto Antonini View PDF HTML (experimental) Abstract: We establish gradient Hölder continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving gradient regularity both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions. Comments: Expanded the introduction with additional examples and references; fixed minor typos, added the Bernstein type inequality Proposition 7.3. Comments are welcome Subjects: Analysis of PDEs (math.AP) MSC classes: 35D30, 35J60, 35J62, 35J66, 35J92, 49N60 Cite as: arXiv:2601.07140 [math.AP] (or arXiv:2601.07140v3 [math.AP] for this version) https://doi.org/10.48550/arXiv.2601.07140 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nonlinear Analysis TMA (2026) Related DOI : https://doi.org/10.1016/j.na.2026.114266 Focus to learn more DOI(s) linking to related resources Submission history From: Carlo Alberto Antonini [ view email ] [v1] Mon, 12 Jan 2026 02:15:28 UTC (104 KB) [v2] Mon, 19 Jan 2026 23:28:50 UTC (107 KB) [v3] Thu, 27 Aug 2026 19:30:08 UTC (111 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-01 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

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