We prove short-time existence and uniqueness of classical solutions in weighted Hölder 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. © Taylor & Francis Group, LLC.

A free boundary problem of fourth order: Classical solutions in weighted hölder spaces / Giacomelli, Lorenzo; H., Knuepfer. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 35:11(2010), pp. 2059-2091. [10.1080/03605302.2010.494262]

A free boundary problem of fourth order: Classical solutions in weighted hölder spaces

GIACOMELLI, Lorenzo;
2010

Abstract

We prove short-time existence and uniqueness of classical solutions in weighted Hölder 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. © Taylor & Francis Group, LLC.
2010
fourth order degenerate parabolic equations; hele-shaw flow; thin-film equations; existence and uniqueness; lubrication theory; thinfilm equations; partial differential equations; free boundary problems; thin fluid films; well posedness
01 Pubblicazione su rivista::01a Articolo in rivista
A free boundary problem of fourth order: Classical solutions in weighted hölder spaces / Giacomelli, Lorenzo; H., Knuepfer. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 35:11(2010), pp. 2059-2091. [10.1080/03605302.2010.494262]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/102824
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