Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane

Antonio Greco; Giuseppe Viglialoro

Applications of Mathematics (2023)

  • Volume: 68, Issue: 2, page 123-142
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Greco, Antonio, and Viglialoro, Giuseppe. "Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane." Applications of Mathematics 68.2 (2023): 123-142. <http://eudml.org/doc/299365>.

@article{Greco2023,
abstract = {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.},
author = {Greco, Antonio, Viglialoro, Giuseppe},
journal = {Applications of Mathematics},
keywords = {Ventcel boundary condition; Laplace-Beltrami operator; composite Sobolev space; well-posedness},
language = {eng},
number = {2},
pages = {123-142},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane},
url = {http://eudml.org/doc/299365},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Greco, Antonio
AU - Viglialoro, Giuseppe
TI - Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 123
EP - 142
AB - 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.
LA - eng
KW - Ventcel boundary condition; Laplace-Beltrami operator; composite Sobolev space; well-posedness
UR - http://eudml.org/doc/299365
ER -

References

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