Removability of singularities for a class of fully non-linear elliptic equations |
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Authors: | María del Mar González |
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Institution: | (1) Mathematics Department 1, The University of Texas at Austin, University Station C1200, Austin, TX 78712, USA |
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Abstract: | In this paper we address the problem of understanding the singularities of the fully non-linear elliptic equation σ
k
(v) = 1. These σ
k
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, σ1 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 Λ as soon as we impose some capacity conditions. The main ingredient is an estimate of the L
∞ norm in terms of a suitable L
p
norm.
Mathematics Subject Classification (2000) 35J60, 53A30 |
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Keywords: | |
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