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Erschienen in:
2002 | OriginalPaper | Buchkapitel
Two Sufficient Conditions for the Regularity of Lateral Boundary for the Heat Equation
verfasst von : Nicolai V. Krylov
Erschienen in: Nonlinear Problems in Mathematical Physics and Related Topics I
Verlag: Springer US
Enthalten in: Professional Book Archive
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The one-dimensional heat equation in the domain x > x(t), t ≥ 0, is considered. We prove the following fact: if the lateral boundary is “Hölder” regular for the heat equation u t = v2u xx for at least one v > 0, then it is regular for the equation with any v > 0. The proof is based on another condition of regularity somewhat close to the exterior cone condition for Laplace’s equation.