Narrow Results

The current state of the vacuum evolution problem in general relativity is reviewed from a perspective of rigorous mathematical results.

We study algebras A → B with the property that H₁(A,B,B)=0. They are quite near to smooth algebras, that is why they are called almost smooth algebras. Some applications to the evolution problem of Eisenbud and Mazur are given.

The main purpose of this work is to study the existence of solutions for a perturbed second-order evolution inclusion involving time-dependent subdifferential operators. Under suitable conditions on the set-valued perturbation, the main result of the paper is proved in the context of a separable Hilbert space. A second-order evolution quasi-variational inequality is also investigated.

The current state of the vacuum evolution problem in general relativity is reviewed from a perspective of rigorous mathematical results.