Search results for " Analisi"
showing 10 items of 1252 documents
The equality case in a Poincaré–Wirtinger type inequality
2016
It is known that, for any convex planar set W, the first non-trivial Neumann eigenvalue μ1 (Ω) of the Hermite operator is greater than or equal to 1. Under the additional assumption that Ω is contained in a strip, we show that β1 (Ω) = 1 if and only if Ω is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.
Serrin-Type Overdetermined Problems: an Alternative Proof
2008
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.
Hessian equations and symmetrization
2005
In this paper we state same comparisons results for solutions to Hessian type equations in dimension n> 2. These results involve convenient rearrangements of solutions that preserve suitable cross-sectional measures of their level sets.
Stability of radial symmetry for a Monge-Ampère overdetermined problem
2008
Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…
La genesi dei poemi omerici
2019
Si tratta della prima analisi sistematica di Iliade e Odissea scritta in una lingua diversa dal tedesco e del primo tentativo di dare un quadro generale delle analisi precedenti. Si cerca di distinguere i vari epe confluiti nei due poemi e come i Bearbeiter finali li hanno messi insieme. Le teorie panoraliste e unitarie vengono rifiutate, mentre vengono accettati i presupposti fondamentali dell’analisi, quale si è praticata per lo più da studiosi germanofoni nel sec. XIX e nella prima metà del XX.
An advanced numerical model for human brain activity investigation
2012
Similarity between morphological characteristics of rills and ephemeral gullies in Sicily, Italy
2009
This paper reports the results of a field investigation aimed to establish morphological similarity between rills and ephemeral gullies. Rill measurements were made on 14 plots having a surface area of 22–352 m2 located on a 14·9% slope and on a plot 6·0 m wide and 22·0 m long having a uniform 22·0% slope. The plots are located on the experimental station for soil erosion measurements, ‘Sparacia’, of the Agricultural Faculty of Palermo University, in Sicily, Italy. All plots are subjected to natural rainfall. The measurements were made immediately following five events between November 2004 and December 2005. The ephemeral gully measurements were made on a cultivated area of about 120 ha, l…