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

Jan Prüss

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 311-327
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Prüss, Jan. "Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces." Mathematica Bohemica 127.2 (2002): 311-327. <http://eudml.org/doc/249061>.

@article{Prüss2002,
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.},
author = {Prüss, Jan},
journal = {Mathematica Bohemica},
keywords = {maximal regularity; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions; Dore-Venni theorem; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions; operator theoretic approach; surface diffusion},
language = {eng},
number = {2},
pages = {311-327},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces},
url = {http://eudml.org/doc/249061},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Prüss, Jan
TI - Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 311
EP - 327
AB - 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.
LA - eng
KW - maximal regularity; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions; Dore-Venni theorem; sectorial operators; interpolation; trace theorems; elliptic and parabolic initial-boundary value problems; dynamic boundary conditions; operator theoretic approach; surface diffusion
UR - http://eudml.org/doc/249061
ER -

References

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  6. Maximal Regularity of Parabolic Problems, Monograph in preparation, 2001. (2001) 
  7. The H -calculus and sums of closed operators, Math. Ann (to appear). (to appear) MR1866491
  8. Fractional powers of operators, Pacific J. Math. 1 (1966), 285–346. (1966) Zbl0154.16104MR0201985
  9. Linear and Quasilinear Equations of Parabolic Type, vol. 23, Transl. Math. Monographs. Amer. Math. Soc., 1968. (1968) MR0241822
  10. On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429–452. (1990) MR1038710
  11. Fractional powers of coercively positive sums of operators, Soviet Math. Dokl. 16 (1975), 1638–1641. (1975) Zbl0333.47010MR0482314

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