We give new regularity results of solutions for the linear wave equation set in a nonsmooth cylindrical domain. Different types conditions are imposed on boundary singular Our study is performed some particular anisotropic H?lder spaces.

We revisit and sharpen the results from our previous work, where we investigated regularity of singular set free boundary in nonlinear obstacle problem. As work Figalli–Serra on classical problem, show that each stratum can be further decomposed into a ‘good’ part an ‘anomalous’ part, former is covered by C 1 , − manifolds, latter lower dimension.

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg [1]. By means of a partial regularity theorem (proved elsewhere), it turns out that we are able to show the existence of a suitable weak solution to the Navier-Stokes equations with a singular set of positive one dimensional Hausdorff measure.

An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyp...