7 research outputs found
Minimality via second variation for microphase separation of diblock copolymer melts
We consider a non local isoperimetric problem arising as the sharp interface
limit of the Ohta-Kawasaki free energy introduced to model microphase
separation of diblock copolymers. We perform a second order variational
analysis that allows us to provide a quantitative second order minimality
condition. We show that critical configurations with positive second variation
are indeed strict local minimizers of the nonlocal perimeter. Moreover we
provide, via a suitable quantitative inequality of isoperimetric type, an
estimate of the deviation from minimality for configurations close to the
minimum in the topology
Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization
Short time existence for a surface diffusion evolution equation with
curvature regularization is proved in the context of epitaxially strained
three-dimensional films. This is achieved by implementing a minimizing movement
scheme, which is hinged on the -gradient flow structure underpinning
the evolution law. Long-time behavior and Liapunov stability in the case of
initial data close to a flat configuration are also addressed.Comment: 44 page
A quantitative second order minimality criterion for cavities in elastic bodies
We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second variation, then it is a strict local minimizer. We also provide a quantitative estimate