Abstract
In the Nagumo-Westphal theory of parabolic inequalities the first step typically involves a strict inequality, and the result for weak inequality is then obtained by introduction of a suitable perturbation. As a rule, it is the latter result that is really wanted. By a double use of the perturbation, bypassing the Nagumo theory, we reach the goal in a single step. Avoiding the Nagumo point is one novelty of the presentation. Another is the use of a discontinuous comparison function in the main theorem.
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References
R. M. Redheffer and W. Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen. Math. Ann. 226 [1977] 155–170. Further references can be found here.
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© 1992 Springer Basel AG
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Redheffer, R.M. (1992). Nagumo theory without the Nagumo point. In: Walter, W. (eds) General Inequalities 6. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7565-3_26
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DOI: https://doi.org/10.1007/978-3-0348-7565-3_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7567-7
Online ISBN: 978-3-0348-7565-3
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