A remark on localized weak precompactness in Banach spaces
We give a characterization of -weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.
A remark on Morrey type regularity for nonlinear elliptic systems of second order
A remark on polyconvex envelopes of radially symmetric functions in dimension
We study polyconvex envelopes of a class of functions related to the function of Kohn and Strang introduced in . We present an example of a function of this class for which the polyconvex envelope may be computed explicitly and we also point out some general features of the problem.
A remark on quasilinear elliptic variational inequalities with discontinuous coefficients
This Note contains the following remark on a recent result by Boccardo and Buttazzo: under the same assumptions, a stronger conclusion, concerning the solvability of variational inequalities, can be obtained.
A remark on the compactness for the Cahn–Hilliard functional
In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.
A remark on the L elevator S-regularity of the minima of functionals of the calculus of variations.
In this note we study the summability properties of the minima of some non differentiable functionals of Calculus of the Variations.
A remark on the local Lipschitz continuity of vector hysteresis operators
It is known that the vector stop operator with a convex closed characteristic of class is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping is Lipschitz continuous on the boundary of . We prove that in the regular case, this condition is also necessary.
A remark on the stability of stationary solutions of parabolic variational inequalities
A Remark on Variational Principles of Choban, Kenderov and Revalski
We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.
A resolution of Simon's maximal monotonicity problem.
A result on equiabsolute integrability
We prove the equiabsolute integrability of a class of gradients, for functions in . The present result appears as the localized version of well-known classical theorems.
A review of the matrix Riccati equation
A Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza locale della soluzione di una equazione di Riccati che si incontra in un problema di controllo ottimale. In ipotesi di regolarità per il costo si prova resistenza globale. Il problema astratto considerato è il modello di alcuni problemi di controllo ottimale governati da equazioni paraboliche con controllo sulla frontiera.
A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Ritz method based on a complementary variational principle
A saddle point theorem for non-smooth functionals and problems at resonance.
A saddle-point approach to the Monge-Kantorovich optimal transport problem
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
A saddle-point approach to the Monge-Kantorovich optimal transport problem
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
A Selection Lemma for Sequences of Measurable Sets, and Lower Semicontinuity of Multiple Integrals.
A selection theory for multiple-valued functions in the sense of Almgren.