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Existence and regularity results for oblique derivative problems for heat equations in an angle
Published online by Cambridge University Press: 14 November 2011
Extract
An initial-boundary-value problem is considered for the heat equation in an infinite angle dθr ⊆ R2 × [0, ∞) with the oblique derivative boundary conditions on the faces λi of the angle:
with either h0 + h1 > 0, or h0 + h1 ≦ 0. The unique solvability of such a problem is proved in appropriate weighted Sobolev spaces according to the sign of h0 + h1. Estimates of the solution are obtained under ‘natural’ restrictions on the opening of the angle.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 47 - 79
- Copyright
- Copyright © Royal Society of Edinburgh 1998
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