Second-order derivative of domain-dependent functionals along Nehari manifold trajectories

On Monadic Parametricity of Second-Order Functionals

How can one rigorously specify that a given ML functional f : (int → int) → int is pure, i.e., f produces no computational effects except those produced by evaluation of its functional argument? In this paper, we introduce a semantic notion of monadic parametricity for second-order functionals which is a form of purity. We show that every monadically parametric f admits a question-answer strate...

Monadic Parametricity of Second-Order Functionals

A Representation Theorem for Second-Order Functionals

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a datatypegeneric representation theorem. More precisely, we prove a representation theorem for a wide class of second-order functionals which are polymorphic over a class of functors. Types polymorphic over a class o...

Second-order shape derivatives along normal trajectories, governed by Hamilton-Jacobi equations

In this paper we introduce a new variant of shape differentiation which is adapted to the deformation of shapes along their normal direction. This is typically the case in the level-set method for shape optimization where the shape evolves with a normal velocity. As all other variants of the orginal Hadamard method of shape differentiation, our approach yields the same first order derivative. H...

Gluing Approximate Solutions of Minimum Type on the Nehari Manifold

In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems. This note is concerned with the procedure of gluing mountain-pass type solutions. The rst procedure to glue mountain-pass type solutions was developed through the work of S er e, and Coti Zelati-Rabinowitz. Th...