

Preprint 21/2004
A Two Well Liouville Theorem
Andrew Lorent
Contact the author: Please use for correspondence this email.
Submission date: 20. Apr. 2004 (revised version: January 2006)
Pages: 48
MSC-Numbers: 74N15
Keywords and phrases: two wells, surface energy, liouville theorem
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Abstract:
In this paper we analyse the structure of approximate solutions to the compatible
two well problem with the constraint that the surface energy of the solution
is less than some fixed constant. We prove a quantitative estimate that can be seen as
a two well analogue of the Liouville theorem of Friesecke James Müller.
Let
be a
diagonal matrix.
Let
. Let
.
Let
be a
invertible bilipschitz
function with
,
.
There exists positive constants and
depending only on
,
,
such that if
and u satisfies the following inequalities
then there exists and
such that