A note on the density of the partial regularity result in the class of viscosity solutions

Authors

  • Disson dos Prazeres Department of Mathematics UFS, 49100-000 São Cristóvão-SE, Brazil
  • Edgard A. Pimentel Department of Mathematics, University of Coimbra – CMUC, 3001-501 Coimbra, Portugal and Department of Mathematics, Pontifical Catholic University of Rio de Janeiro – PUC-Rio, 22451-900, Gávea, Rio de Janeiro-RJ, Brazil
  • Giane C. Rampasso Instituto de Matemática e Computação, Universidade Federal de Itajubá – UNIFEI, Campus Prof. José Rodrigues Seabra, Itajubá-MG, Brasil

DOI:

https://doi.org/10.33044/revuma.2358

Abstract

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its solutions. Distinct conditions on the operator driving the equation lead to density in different topologies. Our findings include applications to nonhomogeneous problems, with variable-coefficient models.

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Published

2022-10-24

Issue

Vol. 63 No. 2 (2022)

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Article

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