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- Title
Convexity for free boundaries with singular term (nonlinear elliptic case).
- Authors
Jeon, Seongmin; Shahgholian, Henrik
- Abstract
We consider a free boundary problem in an exterior domain L u = g (u) in Ω \ K , u = 1 on ∂ K , | ∇ u | = 0 on ∂ Ω , where K is a (given) convex and compact set in R n ( n ≥ 2 ), Ω = { u > 0 } ⊃ K is an unknown set, and L is either a fully nonlinear or the p-Laplace operator. Under suitable assumptions on K and g, we prove the existence of a nonnegative quasi-concave solution to the above problem. We also consider the cases when the set K is contained in { x n = 0 } , and obtain similar results.
- Subjects
NONLINEAR operators
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 1, p451
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02653-3