Removability of singularities for a class of fully non-linear elliptic equations

del Mar Gonz�lez, Mar�a
December 2006
Calculus of Variations & Partial Differential Equations;Dec2006, Vol. 27 Issue 4, p439
Academic Journal
In this paper we address the problem of understanding the singularities of the fully non-linear elliptic equation sk(v) = 1. These sk curvature are defined as the symmetric functions of the eigenvalues of the Schouten tensor of a Riemannian metric and appear naturally in conformal geometry, in fact, s1 is just the scalar curvature. Here we deal with the local behavior of isolated singularities. We give a sufficient condition for the solution to be bounded near the singularity. The same result follows for a more general singular set as soon as we impose some capacity conditions. The main ingredient is an estimate of the L8 norm in terms of a suitable Lp norm.


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