On Radially Symmetric Minima of Nonconvex Functionals

Radial and Nonradial Minimizers for Some Radially Symmetric Functionals

In a previous paper we have considered the functional V (u) = 1 2 ∫ RN | grad u(x)| dx+ ∫ RN F (u(x)) dx subject to ∫ RN G(u(x)) dx = λ > 0 , where u(x) = (u1(x), . . . , uK(x)) belongs to H 1 K(R ) = H(R ) × · · · × H(R) (K times) and | grad u(x)| means ∑K i=1 | gradui(x)|. We have shown that, under some technical assumptions and except for a translation in the space variable x, any global min...

Minima of Non Coercive Functionals

In this paper we study a class of integral functionals defined on H 0 (Ω), but non coercive on the same space, so that the standard approach of the Calculus of Variations does not work. However, the functionals are coercive on W 1,1 0 (Ω) and we will prove the existence of minima, despite the non reflexivity of W 1,1 0 (Ω), which implies that, in general, the Direct Methods fail due to lack of ...

On the Existence of Minima for Nonconvex Variational Problems

We consider the problem of minimizing autonomous, multiple integrals like

The Ricci Flow on Radially Symmetric R

Shape derivatives for minima of integral functionals

For ⌦ varying among open bounded sets in Rn with a Lipschitz boundary @⌦, we consider shape functionals J(⌦) defined as the infimum over a Sobolev space of an integral energy of the kind R ⌦[f(ru) + g(u)], under Dirichlet or Neumann conditions on @⌦. Under fairly weak assumptions on the integrands f and g, we prove that, when a given domain ⌦ is deformed into a one-parameter family of domains ⌦...