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We give some generic properties of non degeneracy for critical points of functionals. We apply these results, obtaining some theorems of multiplicity of solutions for the equation -{epsilon}^2Delta_g u+u=|u|p-2u in M, u in H_g^1(M) where M is a compact Riemannian manifold of dimension n and 2< p<2n/(n-2).
We consider variational integrals of the form $int F(D^2u)$ where $F$ is convex and smooth on the Hessian space. We show that a critical point $uin W^{2,infty}$ of such a functional under compactly supported variations is smooth if the Hessian of $u$ has a small oscillation.
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to $-1$. Existence and properties of a droplet-shaped local energy minimizer are established. A standard mountain pass argume
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $dgeq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Re
We consider critical points of a class of functionals on compact four-dimensional manifolds arising from Regularized Determinants for conformally covariant operators, whose explicit form was derived in [10], extending Polyakovs formula. These corresp
We consider positive critical points of Caffarelli-Kohn-Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for posi