Displaying similar documents to “Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in L p -spaces”

Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in  L p -spaces

Jan Prüss (2002)

Mathematica Bohemica

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Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal L p -regularity is shown. By means of this purely operator theoretic approach, classical results on L p -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem...

The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables

Davide Guidetti (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution u which is bounded with values in C 2 + θ ⁢ Ω ¯ (0 < < 1), with ∂ t ⁡ u bounded with values in C θ ⁢ Ω ¯ .

Linear parabolic problems involving measures.

Herbert Amann (2001)

RACSAM

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Desarrollamos una teoría general para la resolución de ecuaciones lineales de evolución de la forma ü + Au = μ sobre R+, donde -A es el generador infinitesimal de un semigrupo analítico fuertemente continuo y μ es una medida de Radón con valores en un espacio de Banach. Utilizamos la teoría de interpolación-extrapolación de espacios y el teorema de representación de Riesz para tales medidas. Los resultados abstractos son ilustrados mediante aplicaciones...