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math.AP2009★ 3 cited
A Comparison Principle for a Sobolev Gradient Semi-Flow
Timothy Blass, Rafael de la Llave, Enrico Valdinoci
We consider gradient descent equations for energy functionals of the type S(u) = 1/2 < u(x), A(x)u(x) >_{L^2} + \int_Ω V(x,u) dx, where A is a uniformly elliptic operator of order…
math.AP2009
Some elliptic PDEs on Riemannian manifolds with boundary
Yannick Sire, Enrico Valdinoci
The goal of this paper is to investigate some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. We provide several types of results, acc…