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2020 Geometric regularity for elliptic equations in double-divergence form
Raimundo Leitão, Edgard A. Pimentel, Makson S. Santos
Anal. PDE 13(4): 1129-1144 (2020). DOI: 10.2140/apde.2020.13.1129

Abstract

We examine the regularity of the solutions to the double-divergence equation. We establish improved Hölder continuity as solutions approach their zero level-sets. In fact, we prove that α-Hölder continuous coefficients lead to solutions of class 𝒞1, locally. Under the assumption of Sobolev-differentiable coefficients, we establish regularity in the class 𝒞1,1. Our results unveil improved continuity along a nonphysical free boundary, where the weak formulation of the problem vanishes. We argue through a geometric set of techniques, implemented by approximation methods. Such methods connect our problem of interest with a target profile. An iteration procedure imports information from this limiting configuration to the solutions of the double-divergence equation.

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Raimundo Leitão. Edgard A. Pimentel. Makson S. Santos. "Geometric regularity for elliptic equations in double-divergence form." Anal. PDE 13 (4) 1129 - 1144, 2020. https://doi.org/10.2140/apde.2020.13.1129

Information

Received: 8 August 2018; Revised: 18 March 2019; Accepted: 18 April 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07221199
MathSciNet: MR4109902
Digital Object Identifier: 10.2140/apde.2020.13.1129

Subjects:
Primary: 35B65, 35J15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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