Specificity of dimension two in high conductivity problems
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Mon, 04/05/2009 17:00 |
Marc Briane (INSA Rennes & Université Rennes 1) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
This work in collaboration
with J. Casado-Díaz deals with the asymptotic behaviour of
two-dimensional linear conduction problems for which the sequence of
conductivity matrices is bounded from below but not necessarily from
above.
On the one hand, we prove an extension in dimension two of the
classical div-curl lemma, which allows us to derive a H-convergence
type result for any L1-bounded sequence of conductivity matrices.
On the other hand, we obtain a uniform convergence result satisfied
by the minimisers of a sequence of two-dimensional diffusion
energies. This implies the closure for the L2-strong topology of
 -convergence of the sets of equicoercive diffusion energies
without assuming any bound from above. A few counter-examples in
dimension three, connected with the appearance of non-local effects,
show the specificity of dimension two in the two previous compactness
results. |
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