We study minimizers of the energy functional ∫Ω∣∇u∣2+2F(u)dx, where F′(u)≈∣u∣qlogu for some −1<q<0. We prove existence, optimal decay, and non-degeneracy of solutions, from free boundary points. Consequently, we derive the porosity property and an estimate on the Hausdorff dimension of the free boundary.
1
Sharif University of Technology, Tehran, Iran
2
Babol Noshirvani University of Technology, Iran
Morteza Fotouhi; Somayeh Khademloo. A two-phase free boundary with a logarithmic term. Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 45-60. doi: 10.4171/ifb/502
@article{10_4171_ifb_502,
author = {Morteza Fotouhi and Somayeh Khademloo},
title = {A two-phase free boundary with a logarithmic term},
journal = {Interfaces and free boundaries},
pages = {45--60},
year = {2024},
volume = {26},
number = {1},
doi = {10.4171/ifb/502},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/502/}
}
TY - JOUR
AU - Morteza Fotouhi
AU - Somayeh Khademloo
TI - A two-phase free boundary with a logarithmic term
JO - Interfaces and free boundaries
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IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/502/
DO - 10.4171/ifb/502
ID - 10_4171_ifb_502
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