The one phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition
Citations
35 citations
29 citations
Cites background from "The one phase free boundary problem..."
...1The result is in fact established in the more general case of the p-Laplacian in [18] and is generalized to non-constant μ in [19]....
[...]
22 citations
Additional excerpts
...…u defined on a domain D = D a p ⊃ F with ∗ · u p−2 u = 0 weakly in D\F ∗∗ u x → 1 whenever x → y ∈ F and u x → 0 as x → y ∈ D (1.6) ∗ ∗ ∗ u x → a whenever x → y ∈ D This problem was solved in Henrot and Shahgholian (2000a) (see also Henrot and Shahgholian, 2000b, 2002 for related problems)....
[...]
21 citations
Cites background from "The one phase free boundary problem..."
...The treatment of the nonlinear case is more recent and mainly due to Henrot and Shahgholian, see for instance [15]-[18]; see also [3], [14], [23] and references therein....
[...]
19 citations
Cites background from "The one phase free boundary problem..."
...This problem was solved in [10] (see also [11, 12] for related problems)....
[...]
References
18,443 citations
8,299 citations
2,017 citations
1,885 citations
"The one phase free boundary problem..." refers methods in this paper
...Since alsojrujjp is a subsolution to the operator Luj (Lemma 2.5) we can apply the comparison principle to obtainjrujjp vj in Sj .A sj !1we can invoke classical results on stability [ Lan ] (cf....
[...]
1,694 citations
Additional excerpts
...also [Di] for the parabolic case....
[...]