Abstract
In Section 1.2 we mentioned that although the Green functionG Δ2 Ω for the clamped plate boundary value problem
is in general sign changing, it is very hard to display its negative part in numerical simulations or in real world experiments. Moreover, numerical work in nonlinear elliptic fourth order equations suggests that maximum or comparison principles are violated only to a “small extent”. Nevertheless, we do not yet have tools at hand to give this feeling a precise form and, in particular, a quantitative form which might prove to be useful also for nonlinear higher order equations.
Keywords
- Green Function
- Dirichlet Boundary Condition
- Smooth Domain
- Biharmonic Operator
- Order Elliptic Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2010 Springer-Verlag Berlin Heidelberg
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Gazzola, F., Grunau, HC., Sweers, G. (2010). Dominance of Positivity in Linear Equations. In: Polyharmonic Boundary Value Problems. Lecture Notes in Mathematics(), vol 1991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12245-3_6
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DOI: https://doi.org/10.1007/978-3-642-12245-3_6
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