Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Real interpolation with variable exponent
Full text linkWe present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the case of fixed exponent. An application, we give the real interpolation of variable Besov and Lorentz spaces as introduced recently in Almeida and Hästö (J. Funct. Anal. 258 (5) 1628-2655, 2010) and L. Ephremidze et al. (Fract. Calc. Appl. Anal. 11 (4) (2008), 407-420)
On classical n-absorbing submodules
Full text linkIn this paper, we introduce the notion of classical n-absorbing submodules of a module M over a commutative ring R with identity, which is a generalization of classical prime submodules. A proper submodule N of M is said to be classical n-absorbing if whenever a1a2... an+1 m in M, for a1a2... an+1 in R and m in M, then there are n of the ai\u27s whose product with m is in N. We give some basic results concerning classical n-absorbing submodules. Then the classical n-absorbing avoidance theorem for submodules is proved. Finally, classical n-absorbing submodules in several classes of modules are studied
On the approximate controllability of some semilinear partial functional integrodifferential equations with unbonded delay
Full text linkThis work concerns the study of the approximate controllability for some nonlinear partial functional integrodifferential equation with infinite delay arising in the modelling of materials with memory, in the framework of Hilbert spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed is part approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator. An example of applications is given for illustration
Ultra-relativistic limit of extended thermodynamics of rarefied polyatomic gas
Full text linkThe aim of this paper is to evaluate the ultra-relativistic limit of a recent causal theory proposed for polyatomic dissipative relativistic gas. The explicitly expression of characteristic velocities of the hyperbolic system is found in term of the degree of freedom of the gas and compared with the one of monatomic gas
Characterization of perfect Roman domination edge critical trees
Full text linkA perfect Roman dominating function on a graph is a function
satisfying the condition that every vertex with is adjacent to exactly one vertex
for which . The weight of a perfect Roman dominating function is the sum of
the weights of the vertices. The perfect Roman domination number of , denoted by , is
the minimum weight of a perfect Roman dominating function in . In this paper, we study the
graphs for which adding any new edge decreases the perfect Roman
domination number. We call these graphs -edge critical.
The purpose of this paper is to characterize the class of -edge critical trees
Optimality conditions with respect to an ordering map using an exact separation principle: Optimality conditions
Full text linkIn this note, we are concerned with a multiobjective optimization problem. Using a special (nonlinear) scalarization [1], together with an exact separation principle recently introduced by Zheng,Yang and Zou [11], we give necessary optimality conditions for locally weakly nondominated solutions with respect to a given ordering map. To get the results, a nonsmooth sequential Guignard constraint qualication is introduced
Harnack type inequalities for the parabolic logarithmic p-Laplacian equation
Full text linkIn this note, we concern with a class of doubly nonlinear operators whose prototype is
ut − div(|u|m−1|Du|p−2Du) = 0, p > 1, m + p = 2.
In the last few years many progresses were made in understanding the right form of the Harnack inequalities for singular parabolic equations. For doubly nonlinear equations the singular case corresponds to the range m+p < 3. For 3−p/N < m+p < 3, where N denotes the space dimension, intrinsic Harnack estimates hold. In the range 2 < m + p ≤ 3 − p/N only a weaker Harnack form survives. In the limiting case m+p = 2, only the case p = 2 was studied. In this paper we fill this gap and we study the behaviour of the solutions in the full range p > 1 and m = 2 − p
Height estimate and Lipschitz approximation for geodesics in Carnot groups
Full text linkWe prove a height estimate and an approximation with Lipschitz graphs for geodesics in Carnot groups in the small excess regim
On the proof of Hörmander\u27s hypoellipticity theorem
Full text linkThis is a survey paper about the proof of the hypoellipticity theorem by Hörmander (Acta Math. 1967). We will compare three different proofs of this result: the original one by Hörmander, the proof given by Kohn (Proc. Sympos. Pure Math., 1973) and independently by Oleĭnik and Radkevič in their 1973 monograph, and the more recent proof of a special case of this result, concerning sublaplacians on Carnot groups, given by Bramanti and Brandolini (Nonlinear Analysis, 2015)
Mean-convex sets and minimal barriers
Full text linkA mean-convex set is locally a barrier for minimal surfaces but can fail to be a global barrier. In this note we suggest how to extend to general dimensions the results of a previous unpublished manuscript on the characterization of the global barriers for minimal surfaces