On the isoperimetric inequality for minimal surfaces
On the isoperimetric-type problems with current hyperplanes.
On the jump set of solutions of the total variation flow
On the Lavrentieff phenomenon for some classes of Dirichlet minimum points.
On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes
We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting...
On the level sum of two convex functions on Banach spaces.
On the Linear Isoperimetric Inequality.
On the lower semicontinuity of certain integral functionals
Si dimostra che il funzionale è semicontinuo inferiormente su , rispetto alla topologia indotta da , qualora l’integrando sia una funzione non-negativa, misurabile in , convessa in , limitata nell’intorno dei punti del tipo , e tale che la funzione sia semicontinua inferiormente su .
On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems
On the lower semicontinuity of supremal functionals
In this paper we study the lower semicontinuity problem for a supremal functional of the form with respect to the strong convergence in , furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur’s lemma for gradients of uniformly converging sequences is proved.
On the Lower Semicontinuity of Supremal Functionals
In this paper we study the lower semicontinuity problem for a supremal functional of the form with respect to the strong convergence in L∞(Ω), furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly converging sequences is proved.
On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K instead of the whole space as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous...
On the Łojasiewicz exponent at infinity of real polynomials
Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing...
On the maximum principle for optimal control processes described by Hammerstein integral equations with weakly singular kernels
On the Mayer problem. I: General principles
On the Mayer problem. II: Examples
On the Mazur-Orlicz theorem
On the measurability of the conjugate and the subdifferential of a normal integrand.
On the method of least squares of finding eigenvalues of some symmetric operators
On the minima of functionals with linear growth