530 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
Problems for elliptic singular equations with a quadratic gradient term
No full textWe investigate the homogeneous Dirichlet problem for a class of second-order elliptic partial differential equations with a quadratic gradient term and singular data, arising for instance in the theory of non-Newtonian fluids of type Callegari-Nachman and also of heat conduction in electrically conducting materials of type Cohen-Keller. In particular, we study the asymptotic behavior of the solution near the boundary under suitable assumptions on the growth of the coefficients of the equation
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
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
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