A two-phase free boundary with a logarithmic term

被引：0

作者：

Fotouhi, Morteza ^{[1
]}

Khademloo, Somayeh ^{[2
]}

机构：

[1] Sharif Univ Technol, Dept Math Sci, P932 H5X, Tehran, Tehran Province, Iran

[2] Babol Noshirvani Univ Technol, Dept Math, Babol 4714871167, Mazandaran Prov, Iran

来源：

INTERFACES AND FREE BOUNDARIES | 2024年 / 26卷 / 01期

关键词：

Free boundary problems; semilinear elliptic equation; regularity of solutions; REGULARITY;

D O I：

10.4171/IFB/502

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study minimizers of the energy functional integral(Omega) I del uI(2) + 2F(u)dx, where F ' (u) approximate to. IuI(q) log u for some -1 < q < 0. We prove existence, optimal decay, and nondegeneracy of solutions, from free boundary points. Consequently, we derive the porosity property and an estimate on the Hausdorff dimension of the free boundary.

引用

页码：45 / 60

页数：16

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