Regularity of the free boundary in the one-phase Stefan problem: a recent approach

DOI10.6092/issn.2240-2829/14189zbMath1487.35460OpenAlexW4226502457MaRDI QIDQ5071747

Nicolò Forcillo

Publication date: 22 April 2022

Full work available at URL: https://doaj.org/article/281653a88b144d478dbcce9adcce1239

zbMATH Keywords

free boundary problemsfree boundary regularityone-phase Stefan problemimprovement of flatness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Heat equation (35K05) Free boundary problems for PDEs (35R35) Viscosity solutions to PDEs (35D40) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

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• Regularity in a one-phase free boundary problem for the fractional Laplacian
• Free boundary regularity for a problem with right hand side
• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Regularity of the free boundary in parabolic phase-transition problems
• Structural optimization using sensitivity analysis and a level-set method.
• Regularity of the free boundary for the two-phase Bernoulli problem
• Perturbative estimates for the one-phase Stefan problem
• Two-phase problems with distributed sources: regularity of the free boundary
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Elliptic Partial Differential Equations of Second Order
• The Stefan Problem in Several Space Variables

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