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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

M. G. Garroni ,
V. A. Solonnikov  and
M. A. Vivaldi
M. G. Garroni
Affiliation:
Dipartimento di Matematica, Università ‘La Sapienza’, Rome, Italy
V. A. Solonnikov
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Russia
M. A. Vivaldi
Affiliation:
Dipartimento MeMoMat, Università ‘La Sapienza’, Rome, Italy
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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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