Some results on gradient flows of nonconvex functionals in one dimension

  • Giovanni Bellettini (Università di Roma "Tor Vergata")
G3 10 (Lecture hall)


We are concerned with the problem of defining a reasonable notion of global solution to the partial differential equation obtained as the $L2$-gradient flow of an integral functional with an integrand $\phi$ which is nonconvex in the gradient $u_x$. Typical examples of integrands are $\phi(u_x) = \log(1+u_x2)$ and $\phi(u_x) = (1-u_x2)2$, which give raise to backward-forward parabolic equations. We discuss some results related to the approximation of such equations; we construct also a solution for a particularly simple nonconvex integrand. These results are part of a series of papers (mainly in progress) in collaboration with G. Fusco (Univ. l'Aquila), N. Guglielmi (Univ. l'Aquila), M. Novaga (Univ. Pisa), E. Paolini (Univ. Firenze).

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar