Uniform decay estimates for finite-energy solutions of semi-linear elliptic inequalities and geometric applications |
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Authors: | Stefano Pigola Giona Veronelli |
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Institution: | a Dipartimento di Fisica e Matematica, Università dell?Insubria - Como, via Valleggio 11, I-22100 Como, Italy b Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, I-20133 Milano, Italy |
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Abstract: | We prove uniform decay estimates at infinity for solutions 0?u∈Lp of the semilinear elliptic inequality Δu+auσ+bu?0, a,b?0, σ?1, in the presence of a Sobolev inequality (with potential term). This gives a unified point of view in the investigation of different geometric questions. In particular, we present applications to the study of the topology at infinity of parallel mean curvature submanifolds, to the non-compact Yamabe problem, and to estimate the decay rate of the traceless Ricci tensor of conformally flat manifolds. |
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Keywords: | primary 53C21 secondary 35J60 35R45 53C42 |
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