Recent Results on Nonlinear Elliptic Free Boundary Problems

Ferrari, Fausto; Lederman, Claudia; Salsa, Sandro

doi:10.1007/s10013-022-00565-4

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Cited by 2 publications

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“…We have been motivated in this research by the project of extending some regularity results for free boundary problems already known for linear and nonlinear elliptic operators, see [10].…”

Section: Introductionmentioning

confidence: 99%

Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications

Ferrari,

Forcillo

2023

Boll Unione Mat Ital

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“…We have been motivated in this research by the project of extending some regularity results for free boundary problems already known for linear and nonlinear elliptic operators, see [10].…”

Section: Introductionmentioning

confidence: 99%

Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications

Ferrari,

Forcillo

2023

Boll Unione Mat Ital

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Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side

Ferrari,

Lederman

2024

Calc. Var.

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We consider viscosity solutions to two-phase free boundary problems for the p(x)-Laplacian with non-zero right hand side. We prove that flat free boundaries are $$C^{1,\gamma }$$ C 1 , γ . No assumption on the Lipschitz continuity of solutions is made. These regularity results are the first ones in literature for two-phase free boundary problems for the p(x)-Laplacian and also for two-phase problems for singular/degenerate operators with non-zero right hand side. They are new even when $$p(x)\equiv p$$ p ( x ) ≡ p , i.e., for the p-Laplacian. The fact that our results hold for merely viscosity solutions allows a wide applicability.

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Recent Results on Nonlinear Elliptic Free Boundary Problems

Abstract: In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.

Cited by 2 publications

References 65 publications

Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications

Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications

Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side

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