Regularity for fully nonlinear integro-differential operators with kernels of variable orders

[1805.07955] Regularity for fully nonlinear integro-differential operators with kernels of variable orders Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:1805.07955 (math) [Submitted on 21 May 2018] Title: Regularity for fully nonlinear integro-differential operators with kernels of variable orders Authors: Minhyun Kim , Ki-Ahm Lee View PDF HTML (experimental) Abstract: We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in \cite{CS}. Since the order of differentiability of the kernel is not characterized by a single number, we use the constant \begin{align*} C_\varphi = \left( \int_{\mathbb{R}^n} \frac{1-\cos y_1}{\vert y \vert^n \varphi (\vert y \vert)} \, dy \right)^{-1} \end{align*} instead of $2-\sigma$, where $\varphi$ satisfies a weak scaling condition. We obtain the uniform Harnack inequality and Hölder estimates of viscosity solutions to the nonlinear integro-differential equations. Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:1805.07955 [math.AP] (or arXiv:1805.07955v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.1805.07955 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nonlinear Anal. 193 (2020), 111312, 27 pp Related DOI : https://doi.org/10.1016/j.na.2018.07.009 Focus to learn more DOI(s) linking to related resources Submission history From: Minhyun Kim [ view email ] [v1] Mon, 21 May 2018 09:16:41 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 | 2018-05 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)

Related documents

• Regularity for fully nonlinear integro-differential operators with kernels of variable orders#677279
• Boundary regularity for nonlocal operators with kernels of variable orders#677278
• Boundary regularity for nonlocal operators with kernels of variable orders#674081
• On optimal endpoints for integral kernel operators#1070870
• Partial Gaussian bounds for degenerate operators II#246627