Regularity results for a class of obstacle problems under non standard growth conditions

We prove regularity results for minimizers of functionals F(u, Ω) := ∫Ω f(x, u, Du) dx in the class K := {u ∈ W1,p(x)(Ω, R) : u ≥ ψ}, where ψ : Ω → R is a fixed function and f is quasiconvex and fulfills a growth condition of the type L−1|z|p(x) ≤ f(x, ξ, z) ≤ L(1 + |z|p(x)), with growth exponent p : Ω → (1, ∞)

Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of weak solutions in three space dimensions. Here, we aim at studying the mathematical properties of the model in the two-dimensional case. In particular, we can show existence of global in time strong solutions. Moreover, we can admit slightly more general conditions on some material coefficients of the system

Hip fracture. Preliminary results supporting significative correlations between the psychological wellbeing of patients and their relative caregivers

Background and aim. Hip fracture is one of the major causes of loss of self-sufficiency in older patients. The associated caregiving rehabilitation task often falls to the lot of a member of the patient’s family. Our study aims at assessing the relationship between the psychological well-being of patients with hip fracture and their caregivers. Methods. The study was carried-out on 53 elderly patients with hip fracture and their primary caregivers. The Mini Mental State Examination (patient), Activities of Daily Living (patient), Instrumental Activities of Daily Living (patient), Geriatric Depression Scale (patient), Psychological General Well-Being Index (patient/caregiver) and the Caregiver Burden Inventory (caregiver) were administered to each participant. Results. The results revealed significant correlations between stress levels and the psychological well-being of hip-fracture patients and relative caregivers. In particular, the Caregiver Burden Inventory’s total score was negatively related to the patient’s Psychological General Well-Being Index score (p < 0.05) and with Anxiety (p < 0.05), Depressed Mood (p < 0.01), Positive Well-being (p < 0.05) and General Health (p < 0.05) subscale scores, as well as with the patient’s Activities of Daily Living (p < 0.05) score. Patients’ Psychological General Well-Being Index scores were related to the caregivers’ General Health subscale (p < 0.01), and negatively related to Caregiver Burden Inventory Time Dependence (p < 0.05) and Social Burden (p < 0.05) subscales, as well as with the Geriatric Depression Scale score (p < 0.05). Conclusion. A mutual relationship seems to exist between a patient’s psychological well-being and his/her caregiver’s burden. These findings highlight the importance of a bio-psychosocial approach to both patients and caregivers

On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature on the flow are taken into account. In the mathematical model, the evolution of the macroscopic velocity is ruled by the Navier-Stokes system with temperature-dependent viscosity, while the order parameter representing the concentration of one of the components of the fluid is assumed to satisfy a convective Cahn-Hilliard equation. The effects of the temperature are prescribed by a suitable form of the heat equation. However, due to quadratic forcing terms, this equation is replaced, in the weak formulation, by an equality representing energy conservation complemented with a differential inequality describing production of entropy. The main advantage of introducing this notion of solution is that, while the thermodynamical consistency is preserved, at the same time the energy-entropy formulation is more tractable mathematically. Indeed, global-in-time existence for the initial-boundary value problem associated to the weak formulation of the model is proved by deriving suitable a-priori estimates and showing weak sequential stability of families of approximating solutions.Comment: 26 page

An existence result for A P.D.E. with hysteresis, convection and a nonlinear boundary condition

In this paper a partial differential equation containing a continuous hysteresis operator and a convective term is considered. This model equation, which appears in the context of magnetohydrodynamics, is coupled with a nonlinear boundary condition containing a memory operator. Under suitable assumptions, an existence result is achieved using an implicit time discretization scheme

The Gray Matter project: modificating lifestyles to prevent dementia

As dementia aetiology is based on different bio-psychosocial factors, prevention strategies for dementia have recently focused on multi-domain interventions of individuals at risk and/or with a normative cognitive level, encouraging the lifestyle change through combined programs of physical activity, cognitive training, nutrition education and social activities (in chapter 1, a narrative review of these studies is presented). Most of the multidomain intervention aimed on the prevention of cognitive disease are carried on with elderly patients with a mild cognitive decline or on at-risk adult categories. 5 Caregivers of patients with dementia are considered as an at-risk category. The majority of them (86%) are represented by family members (prominently women) who are also defined as “informal caregivers”. They fulfil their caringgiving role from 7 to 11 h a day on average, up to 10-15 h when clinical conditions worsen 10. Informal caregivers have to cope with physical, psychological and social stressors that affect their health conditions and quality of life negatively (Eleuteri et al., 2016). The burdens of caregiving include many things that have been shown to increase the risk of cognitive decline, including chronic stress, social isolation, depression, decreased physical activity, and a shift in eating habits toward more fast food and significantly more weight compared with controls (Vitaliano et al., 1996). This could be connected with the important role that sleep plays between stress and metabolic health (Geiker et al., 2018). Being a caregiver has been found to be a factor affecting negatively sleep quality (Brummett et al., 2006). Interventions to promote positive lifestyles are, therefore, important in order to improve the caregivers’ general health and, specifically, to prevent the cognitive decline. In the second chapter, an article recently published specifies the importance of multimodal interventions in ameliorating caregivers’ health, since complex moderation and mediation effects exist between the different areas involved in the AD risk reduction. The third chapter will, finally, describe the results of the Gray Matter Project, a multidomain pilot RCT, firstly carried out done in Cache County, Utah designed to promote positive changes in lifestyle (exercise, nutrition, cognitive stimulation, social engagement, stress management, and sleep quality), specifically for the purpose of reducing AD risk in family caregivers of elderly with dementia

Das MaGI-Projekt: Elektronische Katalogisierung der griechischen Handschriften Italiens

Größere und kleinere italienische Bibliotheken bewahren ca. 6500 griechische Handschriften. Dazu kommen ca. 4700 Bände der Vatikanischen Bibliothek. Diese Zahlen beruhen auf reinen Schätzungen, weil neuzeitliche Handschriften, in Archiven aufbewahrte Codices und insbesondere die Zahl der wirklich kodikologischen (also nicht nachträglich buchbinderischen) Einheiten unbekannt ist. Das griechische Handschriftenerbe Italiens muss in Umfang und Inhalt also noch genauer bestimmt werden, was jedoch durch das Fehlen angemessener Bestandsnachweise erschwert wird. Diesen Problemen will ein Langzeitprojekt abhelfen, das eine umfassende elektronische Katalogisierung und – zumindest teilweise – Digitalisierung aller griechischen Handschriften in italienischen Bibliotheken zum Ziel hat. Die Arbeit erfolgt dabei ›offen‹ und ›kollaborativ‹ mit Hilfe einer Software, auf der auch das Katalogisierungsprojekt der ›Nuova Biblioteca Manoscritta‹ beruht das seit 2003 die Katalogisierung der mittelalterlichen und neuzeitlichen Handschriften der Region Venezien betreibt. Diese Software kann einfach für die Katalogisierung von Handschriften unterschiedlicher kultureller Herkunft angepasst werden und ist mit dem vom Istituto Centrale per il Catalogo Unico gepflegten Standard ›Manus‹ kompatibel. Die Ergebnisse der Katalogisierung werden den Forschern frei zur Verfügung stehen und können für paläographische, kodikologische, kunsthistorische und philologische Forschungen an den beschriebenen Handschriften benutzt werden. Da vergleichbare nationale oder internationale Projekte zu byzantinischen Handschriften fehlen, wird ›MaGI‹ auch neue Referenzwerke zur Handschriftenbeschreibung erarbeiten und bereitstellen: Thesauri für Autorennamen und Buchtitel der griechischen Klassik und der byzantinischen Zeit. Diese werden sowohl für die Katalogisierung von Handschriften als auch von Drucken in diesem Feld dienen können