Potential estimates for fully nonlinear elliptic equations with bounded ingredients

Author:

Pimentel Edgard A.12,Walker Miguel2

Affiliation:

1. Centre for Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal

2. Pontifical Catholic University of Rio de Janeiro – PUC-Rio, 22451-900, Gávea, Rio de Janeiro-RJ, Brazil

Abstract

<abstract><p>We examine $ L^p $-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $ p_0 &lt; p &lt; 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 <sup>[<xref ref-type="bibr" rid="b10">10</xref>]</sup>.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

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