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- Title
Tangential contact between free and fixed boundaries for variational solutions to variable-coefficient Bernoulli-type free boundary problems.
- Authors
Moreira, Diego; Shrivastava, Harish
- Abstract
In this paper, we show that, given appropriate boundary data, the free boundaries of minimizers of functionals of type J(v; A, λ+, λ-, Ω)= ∫Ω((A(x∇v, ∇v) + ∇(v))dx and the fixed boundary touch each other in a tangential fashion. We extend the results of Karakhanyan, Kenig, and Shahgholian [Calc. Var. Partial Differential Equations 28 (2007), 15-31] to the case of variable coefficients. We prove this result via classification of the global profiles, as per Karakhanyan, Kenig, and Shahgholian [Calc. Var. Partial Differential Equations 28 (2007), 15-31].
- Subjects
PARTIAL differential equations; CALCULUS of variations
- Publication
Interfaces & Free Boundaries, 2024, Vol 26, Issue 2, p217
- ISSN
1463-9963
- Publication type
Article
- DOI
10.4171/IFB/509