1,721,027 research outputs found
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
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
Existence of stable H-surfaces in cones and their representation as radial graphs
Get PDFIn 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 isovolumetric S^2-type stationary surfaces for capillarity functionals
Get PDFCapillarity 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
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
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
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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