184 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
Stationary states for a two-dimensional singular Schrödinger equation
No full textIn questo articolo studiamo problemi di Dirichlet singolari, lineari e semilineari, della forma in , su , dove è un dominio in e o con (o nonlinearità più generali). In tali problemi bidimensionali emergono alcune difficoltà a causa della non validità della disuguaglianza di Hardy in e a causa delle invarianze dell'equazione . Pertanto opportune condizioni su e sono necessarie al fine di garantire l'esistenza di una soluzione positiva. Per esempio, se è una curva non costante passante per l'origine e è una curva non limitata, allora la disuguaglianza di Hardy vale su qualunque dominio contenuto in e si possono ottenere alcuni risultati di esistenza
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
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
Existence and non existence results for a class of nonlinear singular Sturm-Liouville equations
No full textWe study the existence and nonexistence of solutions for a class of equations of the form
−(ωu′)′ = |u|^{p−2}u in R
where p > 2 and ω is a nonnegative continuous function with isolated zeroes of power type
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
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
Measure properties of the set of initial data yielding nonuniqueness for a class of differential inclusions.
No full textExistence 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
- …
