3,814 research outputs found
Bubbles with prescribed mean curvature: The variational approach
No full textLet H:^3→ R be a C^1 mapping such that H(p)→H_∞>0 as |p|→∞. We show that when H satisfies some global conditions then there exists an H-bubble, namely a sphere S in R^3 such that the mean curvature of S at any regular point p∈S equals H(p
Existence of isovolumetric S^2-type stationary surfaces for capillarity functionals
No full textCapillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillarity functional has no volume-constrained -type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points
Rellich inequalities with weights
No full textLet Ω be a cone in R^n with n ≥ 2. For every fixed R we find the best constant in the Rellich inequality for u smooth and vanishing on ∂Ω. We also estimate the best constant for the same inequality for maps with compact support on Ω. Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains
Motivi letterari nei libri per l’infanzia di Paolo Di Paolo
No full textThe article, organised in the form of a discussion, aims to analyse the themes and motifs of Paolo Di Paolo’s works that are addressed to young audiences. The author has recently published a large number of volumes directed just at younger readers. When beholding the titles that constitute the author’s bibliography, the reader is struck by Di Paolo’s predisposition to transform literary classics: as much in Giacomo il signor bambino as in the edition of the Divina Commedia, the author’s goal is to try to reach his new readers. Therefore, Di Paolo proves to be a prolific author of the genre; in fact, in his bibliography, volumes of fairy tales with a classic slant, such as La mucca volante, are listed as well.L’articolo contiene un’analisi di temi e di motivi delle opere di Paolo Di Paolo dirette al pubblico più piccolo. L’autore negli ultimi anni ha pubblicato un cospicuo numero di volumi indirizzati, infatti, proprio ai lettori più giovani. Ciò che stupisce scorgendo i titoli che costituiscono la bibliografia dell’autore, è la predisposizione a trasformare i classici della letteratura: tanto in Giacomo il signor bambino quanto nell’edizione della Divina Commedia l’obiettivo è cercare di raggiungere i lettori più giovani. Di Paolo si dimostra, quindi, un autore prolifico del genere, tant’è che nell’elenco non mancano volumi fiabeschi dal taglio classico come La mucca volante. Analizzare le opere giovanili dello scrittore costituisce un fatto inedito
Symmetry breaking of extremals for the Caffarelli-Kohn-Nirenberg inequalities in a non-Hilbertian setting
No full textWe provide an explicit necessary condition to have that no extremal for the best constant in the Caffarelli-Kohn-Nirenberg inequality is radially symmetric
Weak limit and blow up of approximate solutions to H-systems
No full textLet H be a continuous function on R^3.
Fixing a domain Ω in R^2 we study the behaviour of a sequence (u_n) of approximate solutions to the H-system
Δu=2H(u)u_x∧u_y in Ω.
Under suitable assumptions o H, we show that the weak limit of the sequence (un) solves the H-system and un→u strongly in H^1 apart from a countable set S made by isolated points. Moreover, if in addition H(p)=H_0+o(1/|p|) as |p|→+∞, H_0 a nonzero content, then in correspondence of each point of S we prove that the sequence (u_n) blows either an H-bubble or an H_0-sphere
Existence of stable H-surfaces in cones and their representation as radial graphs
No full textIn this paper we study the Plateau problem for disk-type surfaces contained in conic regions of R3 and with prescribed mean curvature H. Assuming a suitable growth condition on H, we prove existence of a least energy H-surface X spanning an arbitrary Jordan curve Γ taken in the cone. Then we address the problem of describing such surface X as radial graph when the Jordan curve Γ admits a radial representation. Assuming a suitable monotonicity condition on the mapping λ↦λH(λp) and some strong convexity-type condition on the radial projection of the Jordan curve Γ, we show that the H-surface X can be represented as a radial graph
Existence of H-bubbles in a perturbative setting
No full textGiven a C^1 function H: R^3 → R, we look for H-bubbles, i.e., surfaces in R^3 parametrized by the sphere S^2 with mean curvature H at every regular point. Here we study the case H(u)=H_0(u)+∈H_1(u) where H_0 is some "good" curvature (for which there exist H_ 0-bubbles with minimal energy, uniformly bounded in L^∞), ∈ is the smallness parameter, and H_1 is any C^1 functio
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