Abstract

GARCIA CAMACHO, GONZALO  and  POSADA VERA, LILIANA. L^q estimates of functions in the kernel of an elliptic operator and applications. Integración - UIS [online]. 2016, vol.34, n.1, pp.1-21. ISSN 0120-419X.  https://doi.org/10.18273/revint.v34n1-2016001.

In this work, we will find a family of small functions η_y in the Kernel of an operator defined in the intersection of the Sobolev space H^2,q(Sⁿ) with the orthogonal complement in H^1,2(Sⁿ) of the first eigenspace of the laplacian on Sⁿ, parameterized with a variable y belonging to a small ball contained in Bⁿ⁺¹. We will find L_q estimates of these functions and we will use those estimates to find a subcritical solution to the scalar curvature problem on Sⁿ, and a solution of a nonlinear elliptical problem related to that problem, where F_y1 : Sⁿ→ Sⁿ is a centered dilation.

Keywords : Sobolev spaces; conformal deformations; elliptic equations.

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