[2103.15645] Behaviour at infinity for solutions of a mixed boundary value problem via inversion Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2103.15645 (math) [Submitted on 29 Mar 2021] Title: Behaviour at infinity for solutions of a mixed boundary value problem via inversion Authors: Jana Björn , Abubakar Mwasa View a PDF of the paper titled Behaviour at infinity for solutions of a mixed boundary value problem via inversion, by Jana Bj\"orn and Abubakar Mwasa View PDF HTML (experimental) Abstract: We study a mixed boundary value problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u(x))=0$ in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and zero conormal derivative on the rest. We prove the existence and uniqueness of bounded weak solutions to the mixed problem and characterize the regularity of the point at infinity in terms of \p-capacities. For solutions with only Neumann data near the point at infinity we show that they behave in exactly one of three possible ways, similar to the alternatives in the Phragmén--Lindelöf principle. Comments: 21 pages Subjects: Analysis of PDEs (math.AP) MSC classes: Mathematics Subject Classification (2020): Primary: 35J25. Secondary: 35J62, 35B40 Cite as: arXiv:2103.15645 [math.AP] (or arXiv:2103.15645v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2103.15645 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nonlinear Anal. 258 (2025), Paper No. 113816 Related DOI : https://doi.org/10.1016/j.na.2025.113816 Focus to learn more DOI(s) linking to related resources Submission history From: Abubakar Mwasa [ view email ] [v1] Mon, 29 Mar 2021 14:21:43 UTC (25 KB) Full-text links: Access Paper: View a PDF of the paper titled Behaviour at infinity for solutions of a mixed boundary value problem via inversion, by Jana Bj\"orn and Abubakar Mwasa View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2021-03 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