1,721,030 research outputs found
Higher order boundary estimates for blow-up solutions of elliptic equations
No full textWe investigate blow-up solutions of the equation \Delta u = u^p + g(u) in a bounded smooth domain \Omega. If p > 1 and if g satisfies appropriate growth conditions (compared with the growth of t^p) as t
goes to infinity we find optimal asymptotic estimates of the solution u(x) in terms of the distance
of x from the boundary \partial \Omega
Optimization problems for the energy integral of p-Laplace equations
No full textWe study maximization and minimization problems for the energy integral of a sub-linear p-Laplace equation in a domain Omega, with weight chi_D, where D is a variable subset of Omega with a fixed measure alpha. We prove Lipschitz continuity for the energy integral of a maximizer and differentiability for the energy integral of the minimizer with respect to alpha
Maximization of the first eigenvalue in problems involving the bi-Laplacian
No full textThis paper concerns maximization of the first eigenvalue in problems involving the bi-Laplacian under either Navier boundary conditions or Dirichlet boundary conditions. Physically, in the case of N = 2, our equation models the vibration of a nonhomogeneous plate Ω which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension | Ω |, we investigate the location of these materials throughout Ω so as to maximize the first eigenvalue in the vibration of the corresponding plate
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
Symmetry breaking and other features for eigenvalue problems
No full textIn the first part of this paper we discuss a minimization prob- lem where symmetry breaking arise. Consider the principal eigenvalue for the problem −∆u = λχFu in the ball Ba+2 ⊂ RN, where N ≥ 2 and F varies in the annulus Ba+2 \ Ba, keeping a fixed measure. We prove that, if a is large enough, the minimum of the corresponding principal eigenvalue is attained in a subset which is not symmetric. In the second part of the paper we show that the principal eigenvalue of an equation with an indefinite weight in a general bounded domain Ω can be approximated by a functional related to the energy integral of a suitable nonlinear equation; furthermore, we show that a solu- tion of this nonlinear equation approximates, in the H1(Ω) norm, the principal eigenfunction of our problem
Symmetry of solutions to optimization problems related to partial differential equations
No full textWe investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove
existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving plane method to find symmetry results
for solutions of a system. We apply these results to discuss symmetry for the maximal configurations of the previous problem
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
Psoriatic Arthritis and Outcome Measures
No full textFil: Cauli, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Porru, G. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Piga, M. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Vacca, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Mathieu, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; Ital
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