On the comparison principle for second order elliptic equations without first and zeroth order terms

The comparison principle for semicontinuous viscosity sub- and supersolutions of elliptic equations on the form $F(D^2 w,x) = 0$ is established under a new and weaker condition on the operator.Comment: 25 pages, 3 figure

The solution of the ∞\infty-Laplace equation in the square

By using the hodograph transform we are able to solve a Dirichlet problem for the $\infty$-Laplace equation $\Delta_\infty u := \nabla u\mathcal{H} u\nabla u^\top = 0$.Comment: 15 pages, 2 figure

The Infinity-Laplacian in Smooth Convex Domains and in a Square

We extend some theorems for the Infinity-Ground State and for the Infinity-Potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture

Dietary intake of advanced glycation endproducts and risk of hepatobiliary cancers: A multinational cohort study

Advanced glycation endproducts (AGEs) may contribute to liver carcinogenesis because of their proinflammatory and prooxidative properties. Diet is a major source of AGEs, but there is sparse human evidence on the role of AGEs intake in liver cancer etiology. We examined the association between dietary AGEs and the risk of hepatobiliary cancers in the European Prospective Investigation into Cancer and Nutrition prospective cohort (n = 450 111). Dietary intake of three AGEs, Nε -[carboxymethyl]lysine (CML), Nε -[1-carboxyethyl]lysine (CEL) and Nδ -[5-hydro-5-methyl-4-imidazolon-2-yl]-ornithine (MG-H1), was estimated using country-specific dietary questionnaires linked to an AGEs database. Cause-specific hazard ratios (HR) and their 95% confidence intervals (CI) for associations between dietary AGEs and risk of hepatocellular carcinoma (HCC), gallbladder and biliary tract cancers were estimated using multivariable Cox proportional hazard regression. After a median follow-up time of 14.9 years, 255 cases of HCC, 100 cases of gallbladder cancer and 173 biliary tract cancers were ascertained. Higher intakes of dietary AGEs were inversely associated with the risk of HCC (per 1 SD increment, HR-CML = 0.87, 95% CI: 0.76-0.99, HR-CEL = 0.84, 95% CI: 0.74-0.96 and HR-MH-G1 = 0.84, 95% CI: 0.74-0.97). In contrast, positive associations were observed with risk of gallbladder cancer (per 1 SD, HR-CML = 1.28, 95% CI: 1.05-1.56, HR-CEL = 1.17; 95% CI: 0.96-1.40, HR-MH-G1 = 1.27, 95% CI: 1.06-1.54). No associations were observed for cancers of the intra and extrahepatic bile ducts. Our findings suggest that higher intakes of dietary AGEs are inversely associated with the risk of HCC and positively associated with the risk of gallbladder cancer