On weak solutions of semilinear oblique derivative problem for augmented Hessian equations

In this seminar, the speaker will talk about the existence result for semilinear oblique derivative problem for augmented Hessian equations on bounded domains in Euclidean space. In general, the regularity of the solution is $C^2$ in the interior and globally Lipschitz continuous. If there is a good point of the boundary of the domain in the sense of appropriate uniform convexity in the neighbourhood of the point, then the solution is classical near that point. This is a joint work with Neil S. Trudinger.