Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 42, Issue 2, Pages 931-945Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090756521
Keywords
Ventcel boundary condition; pseudodifferential operators; asymptotic analysis; shape dependency
Categories
Funding
- Agence Nationale de la Recherche [JCJC06-139561]
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Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to well-posed variational problems under a sign condition of a coefficient. Nevertheless, situations where this condition is violated appeared in several works. The well-posedness of such problems was still open. This manuscript establishes, in the generic case, the existence and uniqueness of the solution for the Ventcel boundary value problem without the sign condition. Then we consider perforated geometries and give conditions to remove the genericity restriction.
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