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We prove C1regularity for local vectorial minimizers of the nonautonomous functional w ∈ W1,1loc (Ω; RN) 7→ Z Ω b(x) |Dw|p + a(x)|Dw|p log(e + |Dw|)dx, with Ω open subset of Rn, n ≥ 2, p > 1, 0 ≤ a(·) ≤ kakL∞(Ω) < ∞, and 0 < ν ≤ b(·) ≤ L. The result is valid provided that the function a(·) is logDini continuous and that the coefficient b(·) is Dini continuous or it is weakly differentiable and its gradient locally belongs to the Lorentz space Ln,1 (Ω; Rn). [ABSTRACT FROM AUTHOR]

Abstract We consider measure data problems of p -Laplacian type. The measure on the right-hand side has the property that the total variation of a generic ball decays in terms of generic functions of the radius; we show that this condition has a natural relation with gradient integrability properties and we get, as corollary, borderline cases of classic results. [ABSTRACT FROM AUTHOR]

We study the Cauchy-Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the parabolic boundary and quantify the continuity by deriving a modulus. As a byproduct, these a priori regularity results are used to prove the existence of a so-called physical solution. [ABSTRACT FROM AUTHOR]

We analyze a natural approach to the regularity of solutions of problems related to some anisotropic Laplacian operators, and a subsequent extension of the usual De Giorgi classes, by investigating the relation of the functions in such classes with the weak solutions to some anisotropic elliptic equations as well as with the quasi-minima of the corresponding functionals with anisotropic polynomial growth. [ABSTRACT FROM AUTHOR]

We consider solutions to singular parabolic equations with measurable dependence on the ( x , t ) variables and having on the right-hand side a measure satisfying a density condition. We prove that the less the measure is concentrated, the more the gradient is regular, in the Marcinkiewicz scale. We provide local estimates and recover some classic results. [ABSTRACT FROM AUTHOR]

Although the study of Etruscan urbanism is still rather patchy, recent excavations at some settlements in Northern Etruria and the Po Valley allow to reconstruct urban plans with orthogonal axes that are better represented here than elsewhere. In addition to the archaeological surveys of settlements at Spina and Prato-Gonfienti, the new discoveries at Kainua -Marzabotto and the data derived from the metrological analysis recently conducted on its urban plan allow to better contextualize the phenomenon of the orthogonal reorganization, underway during the late sixth century BCE, of various Etruscan cities in the Po Valley. Furthermore, it enables us to reconstruct the different phases ofthe town sfoundation according to practices associated not only with the religious sphere, linked to the Etruscan rite sacred to Dis Pater, but also and above all to the planning of the urban space. The image of a settlement resulting from this analysis indicates a planning achieved through a careful measurement of the landscape and characterized by an urban system designed on a geometric-proportionalb asisb yt heu seo fa l inearu nite qualt ot heA tticf ootof 2 9.6c m. [ABSTRACT FROM AUTHOR]

We consider solutions to degenerate parabolic equations with measurable coefficients, having on the right-hand side a measure satisfying a suitable density condition; we prove integrability results for the gradient in the Marcinkiewicz scale. [ABSTRACT FROM AUTHOR]

We derive a class of potential estimates for elliptic equations with non-standard growth having a measure on the right-hand side; in particular our results allow to interpolate between the pointwise estimates available for solutions to this equation and the ones for the gradient. We allow bounded coefficients in BMO and VMO classes. [ABSTRACT FROM AUTHOR]

We consider a weak solution to the non-linear, parabolic systems of the form ut - div A( x, t, u, Du) = 0, where the vector field A satisfies a Dini-type continuity condition with respect to the variables ( x, t, u), and we prove a partial regularity result for such a solution. Moreover, we give an estimate of the size of the singular set of a solution in terms of a generalized parabolic Hausdorff measure associated to an appropriate modulus of continuity naturally associated to the coefficients of the system. [ABSTRACT FROM AUTHOR]

Background: The role of body composition (lean mass and fat mass) on urine chemistries and bone quality is still debated. Our aim was therefore to determine the effect of lean mass and fat mass on urine composition and bone mineral density (BMD) in a cohort of healthy females.Materials and Methods: 78 female volunteers (mean age 46 ± 6 years) were enrolled at the Stone Clinic of Parma University Hospital and subdued to 24-hour urine collection for lithogenic risk profile, DEXA, and 3-day dietary diary. We defined two mathematical indexes derived from body composition measurement (index of lean mass-ILM, and index of fat mass-IFM) and the cohort was split using the median value of each index, obtaining groups differing only for lean or fat mass. We then analyzed differences in urine composition, dietary intakes and BMD.Results: The women with high values of ILM had significantly higher excretion of creatinine (991 ± 194 vs 1138 ± 191 mg/day, p = 0.001), potassium (47 ± 13 vs 60 ± 18 mEq/day, p < 0.001), phosphorus (520 ± 174 vs 665 ± 186 mg/day, p < 0.001), magnesium (66 ± 20 vs 85 ± 26 mg/day, p < 0.001), citrate (620 ± 178 vs 807 ± 323 mg/day, p = 0.002) and oxalate (21 ± 7 vs 27 ± 11 mg/day, p = 0.015) and a significantly better BMD values in limbs than other women with low values of ILM. The women with high values of IFM had similar urine composition to other women with low values of IFM, but significantly better BMD in axial sites. No differences in dietary habits were found in both analyses.Conclusions: Lean mass seems to significantly influence urine composition both in terms of lithogenesis promoters and inhibitors, while fat mass does not. Lean mass influences bone quality only in limb skeleton, while fat mass influences bone quality only in axial sites. [ABSTRACT FROM AUTHOR]