Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains

In this paper we deal with the multiplication operator u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω), with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients

Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions, to our knowledge. If some eigenvalue is missing, such operators are nonlinear, degenerate, non-uniformly elliptic, neither convex nor concave. Here we prove an interior Lipschitz estimate under a non-standard assumption: that the solution exists in a larger, unbounded domain, and vanishes at infinity. In other words, we need a condition coming from far away. We also provide existence results showing that this condition is satisfied for a large class of solutions. On the occasion, we also extend a few qualitative properties of solutions, known for uniformly elliptic operators, to partial trace operators

Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity

We deal with fully nonlinear second-order equations assuming a superlinear growth inuwith the aim to generalize previous existence and uniqueness results of viscosity solutions in the whole space without conditions at infinity. We also consider the solvability of the Dirichlet problem in bounded and unbounded domains and show a blow-up result

How did COVID-19 affect medical and cardiology journals? A pandemic in literature

BACKGROUND AND AIMS: The spreading speed of the COVID-19 pandemic forced the medical community to produce efforts in updating and sharing the evidence about this new disease, trying to preserve the accuracy of the data but at the same time avoiding the potentially harmful delay from discovery to implementation. The aim of our analysis was to assess the impact of the COVID-19 pandemic on medical literature in terms of proportion of COVID-19-related published papers and temporal patterns of publications within a sample of general/internal medicine and cardiology journals. METHODS: We searched through PubMed scientific papers published from 1 January 2020 to 31 January 2021 about COVID-19 in ten major medical journals, of which five were in general/internal medicine and five in the cardiology field. We analyzed the proportion of COVID-19-related papers, and we examined temporal trends in the number of published papers. RESULTS: Overall, the proportion of COVID-19-related papers was 18.5% (1986/10 756). This proportion was higher among the five selected general/internal medicine journals, compared with cardiology journals (23.8% vs 9.5%). The vast majority of papers were not original articles; in particular, in cardiology journals, there were 28% 'original articles', 17% 'review articles' and 55.1% 'miscellaneous', compared with 20.2%, 5.1% and 74.7% in general/internal medicine journals, respectively. CONCLUSIONS: Our analysis highlights the big impact of the COVID-19 pandemic on international scientific literature. General and internal medicine journals were mainly involved, with cardiology journals only at a later time

On the Mathematical and Geometrical Structure of the Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible Elastodynamics

Using the theory of $1+1$ hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll in Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this class of solutions yields an infinite family of \emph{linear} solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.Comment: 19 page

Tetrad gravity, electroweak geometry and conformal symmetry

A partly original description of gauge fields and electroweak geometry is proposed. A discussion of the breaking of conformal symmetry and the nature of the dilaton in the proposed setting indicates that such questions cannot be definitely answered in the context of electroweak geometry.Comment: 21 pages - accepted by International Journal of Geometric Methods in Modern Physics - v2: some minor changes, mostly corrections of misprint