Local Hölder continuity for doubly nonlinear parabolic equations

• Author(s): Kuusi, Tuomo ; Siljander, Juhana ; Urbano, José Miguel
• Date: 2010
• Persistent ID: http://hdl.handle.net/10316/13697
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Hölder continuity; Caccioppoli estimates; Intrinsic scaling; Harnack's inequality
• Document Type: Preprint
• Language: English

Description

We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling non-trivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.