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Type: Artigo de periódico
Title: Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in R-n
Author: Biagioni, HA
Gramchev, T
Abstract: We propose a unified functional analytic approach to study the uniform analytic-Gevrey regularity and the decay of solutions to semilinear elliptic equations on R-n. First, we develop a fractional calculus for nonlinear maps in Banach spaces of L-P based Gevrey functions, 1<p<infinity. Then we propose an abstract result on uniform analytic Gevrey regularity, which covers as particular cases solitary wave solutions to both dispersive and dissipative equations. We require a priori low H-P(s) (R-n) regularity, with s>s(cr)>0 depending on the nonlinearity. Next, we investigate the type of decay-polynomial or exponential-of the derivatives of solutions to semilinear elliptic equations, provided they decay a priori slowly as o(\x\(-tau)), \x\ --> infinity for some small tau>0. The restrictions, involved in our results, are optimal. In particular, given a hyperplane L, we construct 2d - 2 strongly singular solutions (locally in H-P(s)(R-n) for s<s(cr)) to the semilinear Laplace equation Deltau + cu(d) = 0, whose singularities are concentrated on L. (C) 2003 Elsevier Inc. All rights reserved.
Subject: fractional derivatives
Gevrey spaces
semilinear equations
uniform Gevrey regularity
commutator estimates
iteration inequalities
polynomial decay
exponential decay
strongly singular solutions
Country: EUA
Editor: Academic Press Inc Elsevier Science
Citation: Journal Of Differential Equations. Academic Press Inc Elsevier Science, v. 194, n. 1, n. 140, n. 165, 2003.
Rights: fechado
Identifier DOI: 10.1016/S0022-0396(03)00197-9
Date Issue: 2003
Appears in Collections:Unicamp - Artigos e Outros Documentos

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