Abstract
The passage to the limit in the p-Laplace Equation \(\Delta _pu = 0\) as \(p \rightarrow \infty \) is best done in connexion with the problem of extending Lipschitz boundary values to the whole domain.
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Notes
- 1.
As always, a domain is an open connected set.
- 2.
The convenient notation
is used for the average of a function. Then is increasing with p.
- 3.
It is helpful that weak convergence in \(L^p\) implies weak convergence in \(L^s,\, s< p.\)
- 4.
We have skipped the procedure with the auxiliary intermediate space \(L^s\) as \(s \rightarrow \infty \).
- 5.
See, however, Theorem 4.1.
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Lindqvist, P. (2016). Variational Solutions. In: Notes on the Infinity Laplace Equation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-31532-4_3
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DOI: https://doi.org/10.1007/978-3-319-31532-4_3
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Online ISBN: 978-3-319-31532-4
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