On Green's functions for positive, elliptic differential operators on closed, Riemannian manifolds and some consequences for semi-linear PDE (Q708848)
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scientific article; zbMATH DE number 5800320
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Green's functions for positive, elliptic differential operators on closed, Riemannian manifolds and some consequences for semi-linear PDE |
scientific article; zbMATH DE number 5800320 |
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On Green's functions for positive, elliptic differential operators on closed, Riemannian manifolds and some consequences for semi-linear PDE (English)
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14 October 2010
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The author proves non-negativity of Green's functions for a class of elliptic differential operators over closed Riemannian manifolds employing methods from calculus of variations with a unilateral constraint. Consequences of this result are then explored, with a maximum principle-type result established for a broad class of semi-linear elliptic PDEs. Moreover, the positivity of the principal eigenfunction of an operator in this class is proven as well.
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Green functions
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principal eigenfunctions
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analysis on manifolds
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unilateral constraints
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