Andrea Bonfiglioli

Reduced prevalence of ischemic events and abnormal supraortic flow patterns in patients with liver cirrhosis

Background: A reduced prevalence of cardiovascular diseases has been reported in liver cirrhosis. However, studies focusing on supraortic district of cirrhotic patients are lacking.

Nonlinear Liouville theorems for some critical problems on H-type groups

Abstract In this paper, we provide a non-existence result for a semilinear sub-elliptic Dirichlet problem with critical growth on the half-spaces of any group of Heisenberg-type. Our result improves a recent theorem in (Math. Ann. 315 (3) (2000) 453).

Liouville-type theorems for real sub-Laplacians

Abstract: An inequality generalizing the classical Liouville and Harnack Theorems for real sub-Laplacians ℒ is proved. A representation formula for functions

Fundamental solutions for non-divergence form operators on stratified groups

u

Harnack inequality for non-divergence form operators on stratified groups

for which ℒu is a polynomial is also showed. As a consequence, some conditions are given ensuring that u is a polynomial whenever ℒu is a polynomial. Finally, an application of this last result is given: if ψ is a C2 map commuting with ℒ, then any of its component is a polynomial function.

Splanchnic haemodynamics in patients with coeliac disease: effects of a gluten-free diet

We construct the fundamental solutions Γ and γ for the non-divergence form operators Σ i,j a i,j (x,t)X i X j - ∂ t and Σ i,j a i,j (x)X i X j , where the X i s are Hormander vector fields generating a stratified group G and (a i,j ) i,j is a positive-definite matrix with Holder continuous entries. We also provide Gaussian estimates of r and its derivatives and some results for the relevant Cauchy problem. Suitable long-time estimates of Γ allow us to construct γ using both t-saturation and approximation arguments.

Changes of liver enzymes and bilirubin during ischemic stroke: mechanisms and possible significance

We prove lower bounds for the fundamental solutions of the non-divergence form operators Σ ι,j α i,j (x,t)X i X j -∂ t and Σ i,j α i,j (x) X i X j , where the X i s are Hormander vector fields generating a stratified group G and (a i,j ) i,j is a positive-definite matrix with Holder continuous entries. We then prove an invariant Harnack inequality for such operators. As a byproduct we also study some relevant properties of the Green functions on bounded domains.

Subharmonic functions in sub-Riemannian settings

BACKGROUND Coeliac disease is characterized by structural and functional changes in the small bowel which may also result in haemodynamic changes. AIMS To establish whether splanchnic haemodynamics can be modified by a gluten-free diet. PATIENTS Ten coeliac patients and 10 paired healthy subjects. METHODS Echo-Doppler measurements were made of splanchnic vessels both fasting and after a standard meal before and after 9 months of a gluten-free diet. RESULTS In comparison to controls, coeliac patients had higher superior mesenteric artery blood velocity and flow, with lower resistance indexes and higher portal vein velocity and flow, particularly 3 h after a meal. Postprandial hyperaemia was reduced and delayed in time. Intrasplenic resistance indexes were also significantly lower both fasting and after a meal. After 9 months of a gluten-free diet, no significant differences were observed between coeliac patients and controls, both fasting and after a meal. CONCLUSIONS Splanchnic haemodynamics is significantly changed in coeliac patients, mainly after a meal. On treatment with a gluten-free diet, both fasting and postprandial haemodynamics became normal.

The Dirichlet problem and the inverse mean-value theorem for a class of divergence form operators

BackgroundSmall changes of bilirubin and liver enzymes are often detected during the acute phase of stroke, but their origin and significance are still poorly understood.MethodsOn days 0, 3, 7, and 14 after admission, 180 patients with ischemic stroke underwent serial determinations of bilirubin, GOT, GPT, γGT, alkaline phosphatase, C-reactive protein (CRP) and complete blood count. On days 0 and 7 common bile duct diameter was measured by ultrasound, and on day 3 cerebral infarct volume (IV) was calculated from CT scan slices.ResultsDuring the first week GOT, GPT, γGT (P < 0.001) and CRP (P = 0.03) increased with subsequent plateau, while significant decrements (P < 0.001) concerned unconjugated bilirubin, erythrocytes and haemoglobin. Alkaline phosphatase, direct bilirubin and common bile duct diameter remained stable. IV correlated with CRP, leukocytes, GOT, γGT (r > 0.3, P < 0.001 for all) and direct bilirubin (r = 0.23, P = 0.008). In multivariate analysis only CRP and GOT remained independently associated with IV (P < =0.001). The correlation of IV with GOT increased progressively from admission to day 14. GOT independently correlated with GPT which, in turn, correlated with γGT. γGT was also highly correlated with leukocytes. Unconjugated bilirubin correlated with haemoglobin, which was inversely correlated with CRP.ConclusionsThe changes of bilirubin and liver enzymes during ischemic stroke reflect two phenomena, which are both related to IV: 1) inflammation, with consequent increment of CRP, leukocytes and γGT, and decrease of haemoglobin and unconjugated bilirubin and 2) an unknown signal, independent from inflammation, leading to increasing GOT and GPT levels.

A note on lifting of Carnot groups

In this note we present mean value characterizations of subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution Γ. These characterizations are based on suitable average operators on the level sets of Γ. Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Rado, Beckenbach and Reade. The results presented here generalize and carry forward former results of the authors in [6, 8]. 1 L-subharmonic functions