Elliptic equations on manifolds and isoperimetric inequalities
1990 ◽
Vol 114
(3-4)
◽
pp. 213-227
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Keyword(s):
A Priori
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SynopsisWe consider linear and nonlinear elliptic equations in divergence form on Riemannian manifolds with or without boundary. In the former case we impose a homogeneous Neumann boundary condition. By making use of isoperimetric inequalities for manifolds, we obtain a priori sharp estimates for the decreasing rearrangement of the solutions to such equations. These estimates enable us to derive bounds for suitable norms of the solutions and of their gradients.
2019 ◽
Vol 21
(07)
◽
pp. 1850053
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2007 ◽
Vol 18
(09)
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pp. 1071-1111
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2003 ◽
Vol 133
(2)
◽
pp. 225-235
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2021 ◽
Vol 496
(1)
◽
pp. 124803
Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
2014 ◽
Vol 163
(8)
◽
pp. 1491-1524
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