Convex Solutions to Nonlinear Elliptic and Parabolic Boundary Value Problems.

摘要

This paper contains: (a) A proof that a function on a convex domain whose graph makes zero contact angle with the bounding cylinder and which satisfies an elliptic equation of the appropriate type is convex. (b) A generalization and direct proof of the Brascamp-Lieb result that the first eigenfunction of the Laplacian on a convex domain is Log concave (and so has covex level sets).