"A principal result of this paper (Theorem 3.5) shows that for nonlinear
elasticity in
n > 1 space dimensions, positivity of the second variation
does not imply a strong local minimum even under 'favorable' convexity
hypotheses on the stored-energy function that reduce in one dimension
to convexity in
y
. This is done by developing in
§2 a new
necessary condition for a minimum in mixed problems of the calculus of
variations that we call
quasiconvexity at the boundary; this
condition applies at an appropriate boundary point of the spatial domain,
and is a version of M
ORREY's quasiconvexity condition which is known
to be necessary at an interior point."
