Some remarks about the density of smooth functions in weighted Sobolev spaces.
Some remarks about the -Dirichlet integral
We discuss variational problems for the -Dirichlet integral, non integer, for maps between manifolds, illustrating the role played by the geometry of the target manifold in their weak formulation.
Some remarks and applications of an extension of a lemma of Ky Fan
Some remarks on existence results for optimal boundary control problems
An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
Some remarks on existence results for optimal boundary control problems
An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
Some remarks on isoperimetry of gaussian type
Some remarks on nonlinear functionals
Some remarks on subdifferentiability of convex functions.
Some remarks on sub-differential calculus.
Mean value inequalities are shown for functions which are sub- or super-differentiable at every point.
Some remarks on the boundary regularity for minima of variational problems with obstacles.
Some Remarks on the Homogenization of the Dam Problem.
Some remarks on the optimal design of periodically reinforced structures
Some remarks on the regularity of minimizers of integrals with anisotropic growth
We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
Some remarks on the space of differences of sublinear functions
Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of...
Some remarks on uniqueness and regularity of Cheeger sets
Some remarks on variational problems for functionals with growth
Some results for an optimal control problem with a semilinear state equation
We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
Some results for the reflection problems in Hilbert spaces
Some results on convergence linked to a perturbed boundary optimal control system.
Some Results on Finiteness in Plateau's Problem, Part I.