Sinestrari, Eugenio On the abstract Cauchy problem of parabolic type in spaces of continuous functions. (English) Zbl 0589.47042 J. Math. Anal. Appl. 107, 16-66 (1985). 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. Cited in 3 ReviewsCited in 124 Documents MSC: 47D03 Groups and semigroups of linear operators 47F05 General theory of partial differential operators 35K25 Higher-order parabolic equations 46K15 Hilbert algebras Keywords:generators of analytic semigroups; abstract theory to Cauchy-Dirichlet problems for parabolic; equations; maximal regularity; spaces of Hölder continuous functions; abstract theory to Cauchy-Dirichlet problems for parabolic equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Agmon, S., On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15, 119-147 (1962) · Zbl 0109.32701 [2] Ardito, A.; Ricciardi, P., Existence and regularity for linear delay partial differential equations, Nonlinear Anal., 4, 411-414 (1980) · Zbl 0433.35066 [3] Bers, L.; John, F.; Schechter, M., Partial Differential Equations (1964), Interscience: Interscience New York · Zbl 0126.00207 [4] Berens, H.; Butzer, P. 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