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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 ℝn|
|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 ℝn. First, we develop a fractional calculus for nonlinear maps in Banach spaces of Lp based Gevrey functions, 1 < p < ∞. 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 Hp s(ℝn) regularity, with s > scr > 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 -τ), x → ∞ for some small τ > 0. The restrictions, involved in our results, are optimal. In particular, given a hyperplane L, we construct 2d - 2 strongly singular solutions (locally in Hp s(ℝn) for s < scr) to the semilinear Laplace equation Δu + cud = 0, whose singularities are concentrated on L. © 2003 Elsevier Inc. All rights reserved.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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