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Elliptic equations on manifolds and isoperimetric inequalities

Published online by Cambridge University Press:  14 November 2011

Andrea Cianchi
Andrea Cianchi
Affiliation:
Istituto Matematico “Ulisse Dini”, Viale Morgagni 67A, 50134 Firenze, Italy
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Synopsis

We 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 213 - 227
Copyright
Copyright © Royal Society of Edinburgh 1990

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