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1999 Existence of a solution to a coupled elliptic system with a Signorini condition
Stéphane Gerbi, Raphaèle Herbin, Emmanuelle Marchand
Adv. Differential Equations 4(2): 225-250 (1999). DOI: 10.57262/ade/1366291414


The existence of the solution to an elliptic system arising in electrochemical modelling is proven here. The elliptic system of interest here is composed of two diffusion equations; one of them is posed with a Dirichlet condition which couples it to the other equation on an interface, and a Signorini condition on one of the boundaries. The other one is posed with Neumann conditions, which are also coupled at an interface. The existence of the solution is proven by using Schauder's fixed point theorem, which requires some previous local regularity properties of the solution to the ``Signorini problem".


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Stéphane Gerbi. Raphaèle Herbin. Emmanuelle Marchand. "Existence of a solution to a coupled elliptic system with a Signorini condition." Adv. Differential Equations 4 (2) 225 - 250, 1999.


Published: 1999
First available in Project Euclid: 18 April 2013

zbMATH: 0959.35047
MathSciNet: MR1674347
Digital Object Identifier: 10.57262/ade/1366291414

Primary: 35J65
Secondary: 35B45 , 35Q99

Rights: Copyright © 1999 Khayyam Publishing, Inc.


Vol.4 • No. 2 • 1999
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