Calculus of Variations and Geometric Measure Theory
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M. Amar - D. Andreucci - P. Bisegna - R. Gianni

Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics

created on 16 Jul 2003
modified by amar on 04 Mar 2005

[BibTeX]

Published Paper

Inserted: 16 jul 2003
Last Updated: 4 mar 2005

Journal: Nonlinear Analysis - Real Word Applications
Volume: 6
Pages: 367-380
Year: 2005

Abstract:

We study the existence and uniqueness for an elliptic problem with a nonlinear dynamic boundary condition, relating the conormal derivative of the unknown to the time derivative of its jump across an internal interface. We firstly prove the well-posedness of a suitable linear version of this problem, by means of a classical result in abstract parabolic theory; then, we study the nonlinear case using a fixed point technique.

\noindent Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.


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