Convex solutions to nonlinear elliptic and parabolic boundary value problems

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