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- Title
Short-Time Regularity for the H-Surface Flow.
- Authors
Bögelein, Verena; Duzaar, Frank; Scheven, Christoph
- Abstract
We consider the heat flow associated with the H-surface system given by ∂tu=-2(H °u)D1u× D2u on B × (0,∞), u(., 0) =u0 on B, u= g on ∂ B × (0,∞), for a prescribed bounded and continuous function H :R3→R satisfying an isoperimetric condition of type c for 0<c<1 and time-independent Dirichlet data g of class C1,γ . Here, B ⊂R2 denotes the unit disk. For the global solutions u: B→R3 constructed in a preceding work, we prove short-time regularity in the sense that u and Du are locally Hölder continuous on B × (0, T) up to a singular time T >0. From this, we deduce the existence of a global solution ũ: B × (0,∞)→R3 that is regular except from finitely many singular times.
- Subjects
MATHEMATICAL models of thermodynamics; HEAT transfer; CONTINUOUS functions; ISOPERIMETRICAL problems; DIRICHLET problem; LIPSCHITZ spaces; GEOMETRIC surfaces
- Publication
IMRN: International Mathematics Research Notices, 2015, Issue 12, p3694
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnu042