Browsing by Author "Rossi, JD"
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- ItemA nonlocal diffusion equation whose solutions develop a free boundary(2005) Cortazar, C; Elgueta, M; Rossi, JDLet J : R -> R be a nonnegative, smooth compactly supported function such that integral(R) J(r)dr = 1. We consider the nonlocal diffusion problem
- ItemBoundary blow-up solutions to elliptic systems of competitive type(2004) García-Melián, J; Rossi, JDWe consider the elliptic system Deltau = u(p)v(q), Deltav = u(r)v(s) in Ohm, where p, s > 1, q, r > 0, and Ohm subset of R-N is a smooth bounded domain, subject to different types of Dirichlet boundary conditions: (F) u = lambda, v = mu, (I) u = v = +infinity and (SF) u = +infinity, v = mu on partial derivativeOhm, where lambda, mu > 0. Under several hypotheses on the parameters p, q, r, s, we show existence and nonexistence of positive solutions, uniqueness and nonuniqueness. We further provide the exact asymptotic behaviour of the solutions and their normal derivatives near partial derivativeOhm. Some more general related problems are also studied. (C) 2004 Published by Elsevier Inc.
- ItemOn the existence of extremals for the Sobolev trace embedding theorem with critical exponent(WILEY, 2005) Bonder, JF; Rossi, JDIn this paper, the existence problem is studied for extremals of the Sobolev trace inequality W-1,W-p(Omega) --> L-p* (partial derivativeOmega), where Omega is a bounded smooth domain in R-N, p(*) = p(N - 1)/(N - p) is the critical Sobolev exponent, and 1 < p < N.
- ItemOn the Fucik spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition(2004) Martinez, SR; Rossi, JDIn this paper we prove that there exists a first curve of the Fucik spectrum of the problem Deltapu = \u\(p-2)u in Omega with a nonlinear boundary condition given by \delu\(p-2)partial derivativeu/partial derivativev=alpha(u(+))(p-1)-beta(u(-))(p-1) on the boundary of the domain. We also prove that there exists a sequence of curves of the Fucik spectrum which exist locally in the neighborhood of suitable eigenvalues of the p-Laplacian with a nonlinear boundary condition. Finally, we study a resonance problem with respect to the Fucik spectrum. (C) 2004 Published by Elsevier Ltd.
- ItemSelf-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition(2004) Dávila, J; Rossi, JDWe find existence of a nonnegative compactly supported solution of the problem Deltau = u(alpha) in R-+(N), partial derivativeu/partial derivativev = u on partial derivativeR(+)(N). Moreover, we prove that every nonnegative solution with finite energy is compactly supported and radially symmetric in the tangential variables. (C) 2004 Elsevier Inc. All rights reserved.
- ItemShort time behavior near the boundary for the heat equation with a nonlinear boundary condition(2002) Cortazar, C; Elgueta, M; Rossi, JD
- ItemThe behavior of the best Sobolev trace constant and extremals in thin domains(2004) Bonder, JF; Martínez, S; Rossi, JDIn this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W-1,W-p (Omega) hooked right arrow L-q (partial derivativeOmega) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Omega, W-1,W-p (P(Omega),alpha) hooked right arrow L-q (P(Omega), beta).
- ItemThe best constant for the Sobolev trace embedding from W1,1 (Ω) into L1 (partial derivativeΩ)(2004) Andreu, F; Mazón, JM; Rossi, JDIn this paper we study the best constant, lambda1 (Omega) for the trace map from W-1,W-1 (Omega) into L-1 (partial derivativeOmega). We show that this constant is attained in BV (Omega) when lambda(1) (Omega) < 1. Moreover, we prove that this constant can be obtained as limit when p SE arrow 1 of the best constant of W-1,W-p (Omega) -->. L-p (partial derivativeOmega). To perform the proofs we will look at Neumann problems involving the 1-Laplacian, Delta(1) (u) = div (Du/\Du\). (C) 2004 Published by Elsevier Ltd.
- ItemUniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary(1999) Cortazar, C; Elgueta, M; Rossi, JD