We obtain a comparison principle on annuli, with “catenoid-like” functions, for supersolutions of non-linear elliptic PDEs over exterior domains in a non-positively curved manifold with a pole. This result is applied to get an upper estimate on the growth of such supersolutions and, in particular, of exterior graphs of non-negative mean curvature
On the growth of supersolutions of nonlinear PDE's on exterior domains
IMPERA, DEBORA;PIGOLA, STEFANO
2016-01-01
Abstract
We obtain a comparison principle on annuli, with “catenoid-like” functions, for supersolutions of non-linear elliptic PDEs over exterior domains in a non-positively curved manifold with a pole. This result is applied to get an upper estimate on the growth of such supersolutions and, in particular, of exterior graphs of non-negative mean curvature
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