The limit of <Emphasis Type="Italic">W</Emphasis><Superscript>1,1</Superscript> homeomorphisms with finite distortion

We show that the limit f of a weakly convergent sequence of W ^1,1 homeomorphisms f _j with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity of the distortions is deduced both in case of outer and inner distortion.     

A note on weak convergence in L^{1}_{\rm loc}({\mathbb{R}})

Let be a sequence of Borel measurable functions satisfying, for a function the inequalities

Effect of chitosan and thiolated chitosan coating on the inhibition behaviour of PIBCA nanoparticles against intestinal metallopeptidases

Surface modified nanoparticles composed of poly(isobutylcyanoacrylate) (PIBCA) cores surrounded by a chitosan and thiolated chitosan gel layer were prepared and characterized in previous works. The presence of such biopolymers on the nanoparticle surface conferred those nanosystems interesting characteristics that might partially overcome the gastrointestinal enzymatic barrier, improving the oral administration of pharmacologically active peptides. In the present work, the antiprotease behaviour of this family of core–shell nanoparticles was in vitro tested against two model metallopeptidases present in the gastrointestinal tract (GIT): Carboxypeptidase A -CP A- (luminal protease) and Leucine Aminopeptidase M -LAP M- (membrane protease). As previous step, the zinc-binding capacity of these nanoparticles was evaluated. Interestingly, an improvement of both the zinc-binding capacity and the antiprotease effect of chitosan was observed when the biopolymers (chitosan and thiolated chitosan) were used as coating component of the core–shell nanoparticles, in comparison with their behaviour in solution, thanks to the different biopolymer chains rearrangement. The presence of amino, hydroxyl and thiol groups on the nanoparticle surface promoted zinc binding and hence the inhibition of the metallopeptidases analysed. On the contrary, the occurrence of a cross-linked structure in the gel layer surrounding the PIBCA cores of thiolated formulations, due to the formation of interchain and intrachain disulphide bonds, partially limited the inhibition of the proteases. The low accessibility of cations to the active groups of the cross-linked polymeric shell was postulated as a possible explanation of this behaviour. Results obtained in this work make this family of surface-modified nanocarriers promising candidates for the successfull administration of pharmacologically active peptides and proteins by the oral route.     

An embedding theorem in Lorentz-Zygmund spaces

We study Sobolev embedding theorems in Lorentz-Zygmund spaces. Some limiting cases are considered.Supported by M.U.R.S.T. (1990).     

Very weak solutions to elliptic equations with singular convection term

We study Dirichlet problem for a nonlinear equation with a drift term. Despite the presence of the singular convection term, we establish existence and uniqueness of a solution in spaces larger than the natural one.     

An integral form of the isoperimetric inequality

We study stability for an integral isoperimetric inequality.     

L 2-lower semicontinuity of functionals of quadratic type

Summary A representation formula for the L ²-lower semicontinuous envelope of a quadratic integral of Calculus of Variations is given. Some particular cases are explicited in the details.This paper has been supported by G.N.A.F.A. (Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni).