Variational Inequalities for the Fractional Laplacian

In this paper we study the obstacle problems for the fractional Lapalcian of order s ∈ (0, 1) in a bounded domain \({\Omega }\subset \mathbb {R}^{n}\), under mild assumptions on the data.     

Synthesis of 1-(pyridylalkyl)-1-aza-3,6-diphosphacycloheptanes

Reactions of 1,2-bis[(hydroxymethyl)(phenyl)phosphino]ethane with primary pyridylalkylamines gave earlier unknown 1-aza-3,6-diphosphacycloheptanes containing the pyridyl group in the exocyclic substituent. The reactions were found to be stereoselective, preferentially yielding the racemate with the RR/SS-configuration of the P atoms. A mixture of diastereomers of 3,6-diphenyl-1-[2-(2-pyridyl)ethyl]-1-aza-3,6-diphosphacycloheptane reacted with dichloro(cycloocta-1,5-diene)platinum(II) to give cis-P,P-chelate complexes from the meso-isomer and bridged oligomeric complexes from the racemate.     

On Caffarelli–Kohn–Nirenberg-type Inequalities for the Weighted Biharmonic Operator in Cones

We investigate Caffarelli–Kohn–Nirenberg-type inequalities for the weighted biharmonic operator in cones, both under Navier and Dirichlet boundary conditions. Moreover, we study existence and qualitative properties of extremal functions. In particular, we show that in some cases extremal functions do change sign; when the domain is the whole space, we prove some breaking symmetry phenomena.     

H-superfici con ostacolo

Ricerca parzialmente finanziata sui fondi del Ministero della Pubblica Istruzione (40%).     

Degradation of poly(terphenylenephthalide) at high temperatures

The thermal and thermooxidative degradation of poly(terphenylenephthalide) has been studied by thermal analysis, IR and UV spectroscopy, and mass spectrometry. On the basis of the spectral data and the chemical composition of degradation products, it has been shown that both the thermal and thermooxidative degradations of poly(terphenylenephthalide) are characterized by intramolecular cyclization reactions. Depending on the mode of closure of intermediates generated in the course of thermal decomposition of neighboring phthalide groups (head-to-head or head-to-tail), either phenyl-substituted anthraquinones, fluorenones, and fluorenes or symmetric and nonsymmetric dicyclic compounds containing end anthraquinone, fluorenone, and fluorene groups may be formed. The oxidation of poly(terphenylenephthalide) likewise gives rise to cyclic products—the compounds of xanthone and dibenzofuran series.