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Article

Prüss, Jan
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces. (English). Mathematica Bohemica, vol. 127 (2002), issue 2, pp. 311-327
MSC: 34G10, 35G10, 35K20, 35K90, 45K05, 47D06 | MR 1981536 | Zbl 1010.35064 | DOI: 10.21136/MB.2002.134160
Keywords:
maximal regularity; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions
Summary:
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.
References:
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