Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
32/2002
An example in the gradient theory of phase transitions
Camillo De Lellis
Abstract
We prove by giving an example that when $n\geq 3$ the asymptotic behavior of functionals $\int_\Omega \epsilon |\nabla^2 u|^2+(1-|\nabla u|^2)^2/\epsilon$ is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case is no longer true in higher dimensions.
