1,721,921 research outputs found
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators
Full text linkMaximum Principles on unbounded domains play a crucial rôle in several problems related to linear second-order PDEs of elliptic and parabolic type. In this paper we consider a class of sub-elliptic operators L in RN and we establish some criteria for an unbounded open set to be a Maximum Principle set for L. We extend some classical results related to the Laplacian (by Deny, Hayman and Kennedy) and to the sub-Laplacians on stratified Lie groups (by Bonfiglioli and the second-named author)
An application of a global lifting method for homogeneous Hörmander vector fields to the Gibbons conjecture
No full textIn this paper we exploit a global lifting method for homogeneous Hörmander vector fields in order to extend the Gibbons conjecture to any second-order differential operator LX=∑j=1mXj2, where the Xj’s are linearly independent smooth vector fields on Rn satisfying Hörmander’s rank condition and fulfilling a suitable homogeneity property with respect to a family of non-isotropic dilations. The class of these operators comprehends the sub-Laplacians on Carnot groups, the smooth Grushin-type operators and the smooth Δ λ-Laplacians studied by Franchi, Lanconelli and Kogoj. We also establish a comparison result for the solutions of the semi-linear equation LXu+ f(u) = 0 under suitable assumptions on the function f
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators
Full text linkMaximum Principles on unbounded domains play a crucial role in several problems related to linear second-order PDEs of elliptic and parabolic type. In the present notes, based on a joint work with prof. E. Lanconelli, we consider a class of sub-elliptic operators L in R^N and we establish some criteria for an unbounded open set to be a Maximum Principle set for L. We extend some classical results related to the Laplacian(proved by Deny, Hayman and Kennedy) and to the sub-Laplacians on homogeneous Carnot groups (proved by Bonfiglioli and Lanconelli)
On the existence of weak solutions for singular strongly nonlinear boundary value problems on the half-line
No full textIn the present paper, we consider boundary value problems on the real half-line Λ: = [0 , ∞) of the following form (Φ(a(t,x(t))x′(t)))′=f(t,x(t),x′(t))a.e.onΛ,x(0)=ν1,x(∞)=ν2,where Φ: R→ R is a strictly increasing homeomorphism, a∈ C(Λ× R, R) is nonnegative which can vanish on a set of zero Lebesgue measure and f is a Caratheódory function on Λ× R2. Under very general assumptions on the functions a and f, including an appropriate version of the well-known Nagumo–Wintner growth condition, we prove the existence of at least one solution of the above problem in a suitable Sobolev space. Our approach combines a fixed-point technique with the method of lower/upper solutions
Innovazioni operative e tecnologiche per i terminali intermodali merci: metodologie di valutazione e confronto
No full textQuesta ricerca di dottorato è incentrata sul tema del trasporto intermodale delle merci con particolare focus sui terminal ferro-gomma. Il tema di ricerca è stato scelto in base alla volontà della Comunità Europea di rilanciare il trasporto merci intermodale, che ha portato al finanziamento del progetto di ricerca Capacity4Rail, nell’ambito del 7° programma quadro, con lo scopo di definire le linee guida per il trasporto ferroviario del futuro
Global heat kernels for parabolic homogeneous hörmander operators
Full text linkThe aim of this paper is to prove the existence and several selected properties of a global fundamental Heat kernel Gamma for the parabolic operators H = Sigma(m)(j=1) X-j(2)-partial derivative(t), where X-1,..., X-m are smooth vector fields on R-n satisfying Hormander's rank condition, and enjoying a suitable homogeneity assumption with respect to a family of non-isotropic dilations. The proof of the existence of G is based on a (algebraic) global lifting technique, together with a representation of G in terms of the integral (performed over the lifting variables) of the Heat kernel for the Heat operator associated with a suitable sub-Laplacian on a homogeneous Carnot group. Among the features of G we prove: homogeneity and symmetry properties; summability properties; its vanishing at infinity; the uniqueness of the bounded solutions of the related Cauchy problem; reproduction and density properties; an integral representation for the higher- order derivatives
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems
No full textWe prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of Hirano et al. (J Differ Equ 189(2):487–512, 2003), extending the recent results in Garain (J Geom Anal 33:212, 2023) concerning singular problems and, at the same time, the results in Biagi et al. (A Brezis–Nirenberg type result for mixed local and nonlocal operators, https://arxiv.org/abs/2209.07502, 2023) regarding critical problems
A Liouville-type theorem for elliptic equations with singular coefficients in bounded domains
No full textWe investigate Liouville-type theorems for elliptic equations with a drift and with a potential posed in bounded domains. We provide sufficient conditions on the potential and on the drift term in order to the equation does not admit nontrivial bounded solutions. We also show that such conditions are optimal. Indeed, when they fail, the elliptic equation possesses infinitely many bounded solutions
On the existence of a second positive solution to mixed local-nonlocal concave–convex critical problems
No full textWe prove the existence of a second positive weak solution for mixed local-nonlocal critical semilinear elliptic problems with a sublinear perturbation in the spirit of Ambrosetti et al. (1994)
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