On the abstract Cauchy problem of parabolic type in spaces of continuous functions
The main object of this paper is the study of the problem \[ u'(t)=Au(t)+f(t),\quad t\in [0,T];\quad u(0)=u_ 0 \] when f: [0,T]\(\to E\) (a Banach space), \(u_ 0\in E\) and A: D(A)\(\subseteq E\to E\) verifies all the properties of the generators of analytic semigroups with the possible exception of the density of D(A) in E. This gives the possibility of applying the abstract theory to Cauchy-Dirichlet problems for parabolic equations and obtain maximal regularity results in spaces of Hölder continuous functions.
abstract theory to Cauchy-Dirichlet problems for parabolic
abstract theory to Cauchy-Dirichlet problems for parabolic equations
scientific article; zbMATH DE number 3946979
scientific article