A generalized domain for semigroup generators
Michael G. Crandall · Proceedings of the American Mathematical Society · 1973
A generalized domain $\hat D(A)$ is assigned to a certain class of generators A of semigroups of nonlinear transformations S on Banach spaces. $\hat D(A)$ is then characterized in two ways. $\hat D(A)$ is the set of x such that $S(t)x$ is locally Lipschitz continuous in t or, equivalently, the set of x which can lie in the domain of suitable extensions of A.