@article{Pimentel2023, 
author = {Edgard A. Pimentel and Miguel Walker},
title = {Potential estimates for fully nonlinear elliptic equations with bounded ingredients},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-16},
keywords = {fully nonlinear equations, Lp-viscosity solutions, potential estimates, gradient-regularity estimates},
url = {https://www.sciopen.com/article/10.3934/mine.2023063},
doi = {10.3934/mine.2023063},
abstract = {We examine        L    p  -viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering        p    0    <  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        L    p  -viscosity solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and Giuseppe Mingione [10].}
}