Geodesic
Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane
Applications of Mathematics, Tome 68 (2023) no. 2, pp. 123-142.

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This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a particular case arising in real-world applications and discuss the resulting model.
DOI : 10.21136/AM.2022.0095-21
Classification : 35A01, 35A02, 35J25, 35M12
Keywords: Ventcel boundary condition; Laplace-Beltrami operator; composite Sobolev space; well-posedness 
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     title = {Existence and uniqueness for a two-dimensional {Ventcel} problem modeling the equilibrium of a prestressed membrane},
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Greco, Antonio; Viglialoro, Giuseppe. Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane. Applications of Mathematics, Tome 68 (2023) no. 2, pp. 123-142. doi : 10.21136/AM.2022.0095-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0095-21/

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