We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators’ domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of “almost convex” domains, which apply to do...

In this note, we extend some earlier non-existence, monotonicity and one-dimensionality results of W. Reichel and the author, by replacing the local Lipschitz continuity hypothesis on the non-linearities by a so-called boundedly uniform Lipschitz condition in the magnitude of u.

We study Lipschitz continuity with respect to the parameter of the set of solutions of a parameterized minimax problem on a product Banach space. We present a sufficient condition ensuring that the map which to any value of the parameter assigns the set of solutions of the problem (possibly multi-valued, and unbounded) possesses Lipschitz-like property, introduced by J.-P. Aubin.

Interpolating discrete volume data into a continuous form adapts implicit surface techniques for rendering volumetric iso-surfaces. One such algorithm uses the Lipschitz condition to create an octree representation that accelerates volume rendering. Furthermore, only one preprocessing step is needed to create the Lipschitz-octree representation that accelerates rendering of iso-surfaces for any...