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David John Needham^{*}, John Christopher Meyer
Research output: Contribution to journal › Article › peer-review
In this note, we highlight a difference in the conditions of the classical weak maximum principle and the classical strong maximum principle for linear parabolic partial differential inequalities. We demonstrate, by the careful construction of a specific function, that the condition in the classical strong maximum principle on the coefficient of the zeroth-order term in the linear parabolic partial differential inequality cannot be relaxed to the corresponding condition in the classical weak maximum principle. In addition, we demonstrate that results (often referred to as boundary point lemmas) which conclude positivity of the outward directional derivatives of nontrivial solutions to linear parabolic partial differential inequalities at certain points on the boundary where a maxima is obtained cannot be obtained under the same zeroth-order coefficient conditions as in the classical strong maximum principle.
Original language | English |
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Pages (from-to) | 2081-2086 |
Number of pages | 6 |
Journal | Zeitschrift für angewandte Mathematik und Physik |
Volume | 66 |
Issue number | 4 |
Early online date | 21 Jan 2015 |
DOIs | |
Publication status | Published - Aug 2015 |
Research output: Contribution to journal › Article › peer-review
Research output: Book/Report › Book