We study some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. Our results are classified by the dimension of the manifold and the sign of its Ricci curvature. As a consequence of our results on boundary reactions, we obtain several symmetry and Liouville results for nonlocal equations.
Some elliptic PDEs on Riemannian manifolds with boundary / Y. Sire, E. Valdinoci. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - 248:2(2010), pp. 475-492. [10.2140/pjm.2010.248.475]
Some elliptic PDEs on Riemannian manifolds with boundary
E. Valdinoci
2010
Abstract
We study some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. Our results are classified by the dimension of the manifold and the sign of its Ricci curvature. As a consequence of our results on boundary reactions, we obtain several symmetry and Liouville results for nonlocal equations.
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