A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds
Keyword(s):
AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.
2005 ◽
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pp. 1863-1881
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1965 ◽
Vol 20
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pp. 373-384
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Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
2014 ◽
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pp. 1491-1524
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1989 ◽
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2015 ◽
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pp. 2693-2712
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pp. 285-312
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2004 ◽
Vol 3
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pp. 395-415
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