On a degenerate parabolic problem in Hölder spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Hölder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Hölder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.