A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Holder Spaces

作者：Giacomelli Lorenzo; Knuepfer Hans

来源：Communications in Partial Differential Equations, 2010, 35(11): 2059-2091.

DOI：10.1080/03605302.2010.494262

• Existence and uniqueness
• Fourth order degenerate parabolic equations
• Free boundary problems
• Hele-Shaw flow
• Lubrication theory
• Thin-film equations
• Thin fluid films

We prove short-time existence and uniqueness of classical solutions in weighted Holder spaces for the thin-film equation with linear mobility, zero contact angle, and compactly supported initial data. We furthermore show regularity of the free boundary and optimal regularity of the solution in terms of the regularity of the initial data. Our approach relies on Schauder estimates for the operator linearized at the free boundary, obtained through a variant of Safonov's method that is solely based on energy estimates.

• 出版日期2010