Geodesic
Tangential contact between free and fixed boundaries for variational solutions to variable-coefficient Bernoulli-type free boundary problems
Diego Moreira1 ; Harish Shrivastava2 orcid
1Universidade Federal do Ceará, Fortaleza, Brazil
2Gandhi Institute of Technology and Management (GITAM), Bangalore, India
Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 217-243

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DOI

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〉+Λ(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].
DOI : 10.4171/ifb/509
Classification : 49J05, 35B65, 35Q92, 35Q35
Mots-clés : variational calculus, Bernoulli-type free boundary problems, boundary behavior, Alt–Caffarelli–Friedman-type minimizers

Diego Moreira  1   ; Harish Shrivastava  2

1 Universidade Federal do Ceará, Fortaleza, Brazil
2 Gandhi Institute of Technology and Management (GITAM), Bangalore, India 
Diego Moreira; Harish Shrivastava. Tangential contact between free and fixed boundaries for variational solutions to variable-coefficient Bernoulli-type free boundary problems. Interfaces and free boundaries, Tome 26 (2024) no. 2, pp. 217-243. doi: 10.4171/ifb/509
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