Optimal $C^{1,α}$ regularity up to the boundary for fully nonlinear elliptic equations with double phase degeneracy

[2604.04776] Optimal $C^{1,α}$ regularity up to the boundary for fully nonlinear elliptic equations with double phase degeneracy Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2604.04776 (math) [Submitted on 6 Apr 2026 ( v1 ), last revised 19 Oct 2026 (this version, v4)] Title: Optimal $C^{1,α}$ regularity up to the boundary for fully nonlinear elliptic equations with double phase degeneracy Authors: Junior da Silva Bessa , Jehan Oh View PDF HTML (experimental) Abstract: In this paper we establish optimal $C^{1,\alpha}$ regularity up to the boundary for viscosity solutions of fully nonlinear elliptic equations with double phase degeneracy law and oblique boundary conditions. The approach developed here relies on first deriving uniform boundary Hölder estimates for perturbed models with oblique boundary data in ``almost $C^{1}$-flat'' domains. Building upon these estimates, the desired regularity is obtained through a compactness and stability framework for viscosity solutions. As a byproduct of our analysis, we determine the optimal Hölder exponent for solutions when the governing operator is quasiconvex or quasiconcave. In addition, we establish an improved regularity result along vanishing points of the source term. Subjects: Analysis of PDEs (math.AP) MSC classes: 35B65, 35D40, 35J25, 35J70 Cite as: arXiv:2604.04776 [math.AP] (or arXiv:2604.04776v4 [math.AP] for this version) https://doi.org/10.48550/arXiv.2604.04776 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jehan Oh [ view email ] [v1] Mon, 6 Apr 2026 15:49:01 UTC (19 KB) [v2] Fri, 28 Aug 2026 07:48:07 UTC (25 KB) [v3] Wed, 14 Oct 2026 13:27:20 UTC (27 KB) [v4] Mon, 19 Oct 2026 07:19:13 UTC (27 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-04 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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