Abstract
The Laplace equation \(\Delta u=0\).
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Notes
- 1.
The terminology comes from fluid dynamics. An equation of the type
$$\frac{\partial v}{\partial t}\,=\, {\text {div}}(\rho (|\nabla v|)\nabla v)$$is called singular, when it so happens that the diffusion \(\rho = \infty \) and degenerate when \(\rho = 0.\) Notice also the expansion
$$\rho (|\nabla v|) = |\nabla v|^{p-2}\left( c_1 + c_2|\nabla v|+ c_2|\nabla v|^2 \cdots \right) .$$ - 2.
“The more ambitious plan may have more chances of success”, G. Polya, How to Solve It, Princeton University Press, 1945.
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Lindqvist, P. (2019). Introduction. In: Notes on the Stationary p-Laplace Equation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-14501-9_1
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DOI: https://doi.org/10.1007/978-3-030-14501-9_1
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