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https://hdl.handle.net/10316/114886
Title: | Potential estimates for fully nonlinear elliptic equations with bounded ingredients | Authors: | Pimentel, Edgard A. Walker, Miguel |
Keywords: | fully nonlinear equations; Lp-viscosity solutions; potential estimates; gradient-regularity estimates | Issue Date: | 2023 | Publisher: | American Institute of Mathematical Sciences | Project: | UIDB/00324/2020 FAPERJ (# E-26/201.390/2021) FAPERJ (# E-26/201.647/2021) |
Serial title, monograph or event: | Mathematics In Engineering | Volume: | 5 | Issue: | 3 | Abstract: | We examine Lp-viscosity solutions to fully nonlinear elliptic equations with boundedmeasurable ingredients. By considering p0 < p < d, we focus on gradient-regularity estimates stemming from nonlinear potentials. We find conditions for local Lipschitz-continuity of the solutions and continuity of the gradient. We survey recent breakthroughs in regularity theory arising from (nonlinear) potential estimates. Our findings follow from – and are inspired by – fundamental facts in the theory of Lp-viscosity solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and Giuseppe Mingione [10]. | URI: | https://hdl.handle.net/10316/114886 | ISSN: | 2640-3501 | DOI: | 10.3934/mine.2023063 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Potential estimates for fully nonlinear elliptic equations with bounded ingredientsy.pdf | 353.56 kB | Adobe PDF | View/Open |
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