A semilinear elliptic problem containing both a singularity and a critical growth term is considered in a bounded domain of R n : existence results are obtained by variational methods. The solvability of the problem depends on the space dimension n and on the coefficient of the singularity; the results obtained describe the behavior of critical dimensions and nonresonant dimensions when the BrezisNirenberg problem is modified with a singular term.

Abstract. Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with homogeneity of order −1.

SummaryWe study the spectrum of a biharmonic Steklov eigenvalue problem in a bounded domain of R

Clinical features and natural history of coronavirus disease 2019 (COVID-19) differ widely among different countries and during different phases of the pandemia. Here, we aimed to evaluate the case fatality rate (CFR) and to identify predictors of mortality in a cohort of COVID-19 patients admitted to three hospitals of Northern Italy between March 1 and April 28, 2020. All these patients had a confirmed diagnosis of SARS-CoV-2 infection by molecular methods. During the study period 504/1697 patients died; thus, overall CFR was 29.7%. We looked for predictors of mortality in a subgroup of 486 patients (239 males, 59%; median age 71 years) for whom sufficient clinical data were available at data cut-off. Among the demographic and clinical variables considered, age, a diagnosis of cancer, obesity and current smoking independently predicted mortality. When laboratory data were added to the model in a further subgroup of patients, age, the diagnosis of cancer, and the baseline PaO2/FiO2 ratio were identified as independent predictors of mortality. In conclusion, the CFR of hospitalized patients in Northern Italy during the ascending phase of the COVID-19 pandemic approached 30%. The identification of mortality predictors might contribute to better stratification of individual patient risk.