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Geometric regularity
for elliptic equations in double-divergence form
Raimundo Leitão, Edgard A. Pimentel and Makson S. Santos |
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Vol. 13 (2020), No. 4, 1129–1144
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Abstract |
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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 -Hölder continuous coefficients lead to solutions of class , locally. Under the assumption of Sobolev-differentiable coefficients, we establish regularity in the class . 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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Keywords
double-divergence equations, geometric regularity, improved
regularity at zero level-sets
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Mathematical Subject Classification 2010
Primary: 35B65, 35J15
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Milestones
Received: 8 August 2018
Revised: 18 March 2019
Accepted: 18 April 2019
Published: 13 June 2020
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Authors |
| Raimundo Leitão | |
| Department of Mathematics Universidade Federal do Ceara Fortaleza Brazil |
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| Edgard A. Pimentel | |
| Department of Mathematics Pontifical Catholic University of Rio de Janeiro Rio de Janeiro Brazil |
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| Makson S. Santos | |
| Department of Mathematics Pontifical Catholic University of Rio de Janeiro Rio de Janeiro Brazil |
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