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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  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. 10.1007/BF02570748, Math. Z. 203 (1990), 429–452. (1990) MR1038710DOI10.1007/BF02570748
  11. Fractional powers of coercively positive sums of operators, Soviet Math. Dokl. 16 (1975), 1638–1641. (1975) Zbl0333.47010MR0482314

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