In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with [Formula: see text], text] or which extends in [A. Alvino, C. Nitsch Trombetti, A Talenti result to elliptic problems Robin boundary conditions, Comm. Pure Appl. Math. 76(3) (2023) 585–603]. Furthermore, as applica...

Abstract In data assimilation (DA), the estimation of background error covariance operator is a classical and still open topic. However, this often modeled using empirical information. order to exploit at best potential knowledge physics, present study proposes method derive operators from underlying equations. addition, Green’s kernels can be used model are naturally linked them. Therefore, eq...

The avalanche-dynamics approach has a long history in avalanche prediction. In the absence of computers, scientists and engineers focused on idealized models in which avalanches were seen as rigid sliding blocks. Although the resulting governing equation was very simple, the use of empirical rules made the model outcomes quite realistic, the errors being counterbalanced by common sense and expe...