Existence of solutions to a fully nonlinear free transmission problem

Pimentel, Edgard A.; Święch, Andrzej

doi:10.1016/j.jde.2022.02.057

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Introduction4

Main Assumptions and Preliminary Materials1

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2022

2024

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Cited by 8 publications

(5 citation statements)

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“…(Ellipticity) There exists 0 < µ < 1 such that for every x ∈ Ω we have µ ≤ A ± (x) ≤ 1 µ . Recent developments in the case of free transmission problems can be found in [1], [20], [14], [7], [23] and [19]. In [20], we have shown optimal regularity for solutions to a variational free transmission problem (for the case p = 2).…”

Section: Introductionmentioning

confidence: 85%

Optimal regularity for variational solutions of free transmission problems

Moreira

Shrivastava²

2023

Journal de Mathématiques Pures et Appliquées

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Section: Introductionmentioning

confidence: 85%

Optimal regularity for variational solutions of free transmission problems

Moreira

Shrivastava²

2023

Journal de Mathématiques Pures et Appliquées

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“…For some regularity results on the Isaacs equation under perturbative methods (following the program launched in [4]), we refer the reader to [20]. For a remark on variants of A 2.3, we mention [22,Remark 1].…”

Section: Main Assumptions and Preliminary Materialsmentioning

confidence: 99%

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

Prazeres¹,

Pimentel²,

Rampasso³

2022

Revista De La Unión Matemática Argentina

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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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“…Then a fixed-point argument ensures the existence of viscosity solutions to the Dirichlet problem associated with (1.2). For a similar approach in the context of free transmission problems, see [26].…”

Section: Introductionmentioning

confidence: 99%