Regularity of the free boundary for the one phase Hele--Shaw problem

DOI10.1016/j.jde.2005.07.003zbMath1087.76024OpenAlexW2084057876MaRDI QIDQ2368704

Inwon Christina Kim

Publication date: 28 April 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.07.003

zbMATH Keywords

Lipschitz continuous boundary

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Other free boundary flows; Hele-Shaw flows (76D27)

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Cites Work

• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• The regularity of free boundaries in higher dimensions
• Regularity of the free boundary in parabolic phase-transition problems
• Uniqueness and existence results on the Hele-Shaw and the Stefan problems
• Local existence of classical solutions to the well-posed Hele-Shaw problem.
• Long time regularity of solutions of the Hele--Shaw problem
• All Time Smooth Solutions of the One-Phase Stefan Problem and the Hele-Shaw Flow
• Nonlinear analytic semiflows
• Regularity of one-phase Stefan problem near Lipschitz initial data
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• A variational inequality approach to Hele-Shaw flow with a moving boundary
• Classical Solutions of Multidimensional Hele--Shaw Models
• Global in time solution to the Hele-Shaw problem with a change of topology
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
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