BIRS Workshop Lecture Videos
The symmetry of stable solutions of semilinear elliptic equations Nordmann, Samuel
Consider a general semilinear elliptic equation with Neumann boundary conditions. A seminal result of Casten, Holland (1978) and Matano (1979) states that, if the domain is convex and bounded, any stable solution is constant. In this talk, we will investigate whether this classification result extends to convex unbounded domains, or to some non-convex domains. These questions involve the geometry of the domain in a rather intricate way. In particular, our results recover and extend some classical results on De Giorgi's conjecture about the classification of stable solutions of the Allen-Cahn equation in $R^n$.
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