Geodesic
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 311-327

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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 with surface diffusion for the diffusion equation is included.
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.
DOI : 10.21136/MB.2002.134160
Classification : 34G10, 35G10, 35K20, 35K90, 45K05, 47D06
Keywords: maximal regularity; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions 
Prüss, Jan. Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 311-327. doi: 10.21136/MB.2002.134160
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