86,690 research outputs found
Dialogo con Olga Sedakova e Antonella Anedda. Su Dante (la cultura russa) e la poesia contemporanea
No full textIllustrazione delle opere delle poetesse Sedakova e Anedda in relazione all'opera di Dante Alighier
Second-order boundary estimates for solutions to singular elliptic equations
No full textLet be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary in the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the singular semilinear equation . Under appropriate growth conditions on as approaches zero, we find an asymptotic expansion up to the second order of the solution in terms of the distance from to the boundary
Optimal location of resources and Steiner symmetry in a population dynamics model in heterogeneous environments
No full textThe subject of this paper is inspired by Cantrell and Cosner (1989) and Cosner, Cuccu and Porru (2013). Cantrell and Cosner (1989) investigate the dynamics of a population in heterogeneous environments by means of diffusive logistic equations. An important part of their study consists in finding sufficient conditions which guarantee the survival of the species. Mathematically, this task leads to the weighted eigenvalue problem in a bounded smooth domain , , under homogeneous Dirichlet boundary conditions, where and . The domain represents the environment and , called the local growth rate, says where the favourable and unfavourable habitats are located. Then, Cantrell and Cosner (1989) consider a class of weights corresponding to environments where the total sizes of favourable and unfavourable habitats are fixed, but their spatial arrangement is allowed to change; they determine the best choice among them for the population to survive.
In our work we consider a sort of refinement of the result above. We write the weight as sum of two (or more) terms, i.e. , where and represent the spatial densities of the two resources which contribute to form the local growth rate . Then, we fix the total size of each resource allowing its spatial location to vary. As our first main result, we show that there exists an optimal choice of and and find the form of the optimizers. Our proof relies on some results in Cosner, Cuccu and Porru (2013) and on a new property (to our knowledge) about the classes of rearrangements of functions. Moreover, we show that if is Steiner symmetric, then the best arrangement of the resources inherits the same kind of symmetry. (Actually, this is proved in the more general context of the classes of rearrangements of measurable functions
Boundary behaviour for solutions of boundary blow-up problems in a borderline case
No full textWe investigate boundary blow-up solutions of the equation \Delta u = f (u) in a bounded domain Ω ⊂ R^N under the condition
that f (t) has a relatively slow growth as t goes to infinity. We show how the mean curvature of the boundary ∂Ω appears in the
asymptotic expansion of the solution u(x) in terms of the distance of x from ∂Ω
Boundary estimates for solutions of weighted semilinear elliptic equations
No full textLet b(x) be a positive function in a bounded smooth domain Ω ⊂ RN, and let f(t) be a positive non decreasing function on (0,∞) such that limt→∞ f(t) = ∞. We investigate boundary blow-up solutions of the equation ∆u = b(x)f(u). Under appropriate conditions on b(x) as x approaches ∂Ω and on f(t) as t goes to infinity, we find a second order approximation of the solution u(x) as x goes to ∂Ω.
We also investigate positive solutions of the equation ∆u+(δ(x))2lu−q = 0 in Ω with u = 0 on ∂Ω, where l ≥ 0, q > 3 + 2l and δ(x) denotes the distance from x to ∂Ω. We find a second order approximation of the solution u(x) as x goes to ∂Ω
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases
No full textLet be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary on the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the equation . Under appropriate growth conditions on as approaches zero, we find asymptotic expansions up to the second order of the solution in terms of the distance from to the boundary
Symmetry and regularity of an optimization problem related to a nonlinear BVP
No full textWe consider the functional where is the unique nontrivial weak solution of the boundary-value problem where is a bounded smooth domain. We prove a result of Steiner symmetry preservation and, if , we show the regularity of the level sets of minimizers
Second order estimates for boundary blow-up solutions of elliptic equations
No full textWe investigate blow-up solutions of the equation Δu = f(u) in a bounded smooth domain Ω ⊂ RN. Under appropriate growth conditions on f(t) as t goes to infinity we show how the mean curvature of the boundary ∂Ω appears in the second order term of the asymptotic expansion of the solution u(x) as x goes to ∂Ω
Estimates for boundary blow-up solutions of semilinear elliptic equations
No full textWe investigate boundary blow-up solutions of the equation \Delta u = f(u)
in a bounded smooth domain \Omega \subset R^N: Under the condition that f(t) grows
exponentially as t goes to infinity we show how the mean curvature of the
boundary \partial \Omega appears in the asymptotic expansion of the solution u(x) in
terms of the distance of x from the boundary \partial \Omega
Proposta metodologica per l’analisi delle tecniche costruttive altomedievali in Sardegna
No full textThis article outlines the historiography related to the three big domed buildings, erected in Sardinia in the early Middle Ages; it also suggests a survey of the building
techniques utilized in the lesser churches constructed in the long period preceding the spread
of the distinctive features of Romanesque architecture in Sardinia. Holding as an example the church of “Sant’Antioco di Bisarcio (SS)”, which highlights the technological modification
turned up between the two constructional steps of the building, it suggests an overview of the Sardinian building techniques of the early Middle Ages, based upon the stratigraphic analysis of the wall
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