Rearrangements of Functions, Maximization of Convex Functionals, and Vortex Rings.
We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation where the left-hand side is a Leray-Lions operator from into with , is a Carathéodory function which grows like and is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of .