Title: On the regularity for the Dirichlet problem for degenerate Hessian equations
Speaker: Wei Zhou, University of Minnesota
Seminar Type: PDE
Abstract: We consider the Dirichlet problem for positively homogeneous, degenerate elliptic, concave (or convex) Hessian equations. Under natural and necessary conditions on the geometry of the domain, with the C^{1,1}-boundary data, we establish the interior C^{1,1}-regularity of the unique (admissible) solution, which is optimal even if the boundary data is smooth. Both real and complex cases are studied by the unified (Bellman equation) approach. If time permits, we shall also discuss the optimal interior C^{0,1}-regularity of the viscosity solution to the Dirichlet problem for certain nonconvex degenerate Hessian equations.
