MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 311-327 (2002)

Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces

Jan Prüss

Jan Prüss, Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser Str. 5, D-60120 Halle, Germany, e-mail:

Abstract: 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 with surface diffusion for the diffusion equation is included.

Keywords: maximal regularity, sectorial operators, interpolation, trace theorems, elliptic and parabolic initial-boundary value problems, dynamic boundary conditions

Classification (MSC2000): 35K20, 35G10, 45K05, 47D06

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