# Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in ${L}_{p}$-spaces

Mathematica Bohemica (2002)

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

## Access Full Article

top## Abstract

top## How to cite

topPrüss, 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

top- Sommes d’opérateurs linéaires et équations différentielles opérationelles, J. Math. Pures Appl. 54 (1975), 305–387. (1975) MR0442749
- On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 189–201. (1987) MR0910825
- Analytic solutions of the Stefan problem with Gibbs-Thomson correction, (to appear). (to appear)
- Analytic solutions of the free boundary value problem for the Navier-Stokes equation, (to appear). (to appear)
- Spaci di trace e applicazioni, Rend. Math. 5 (1972), 657–729. (1972) MR0341059
- Maximal Regularity of Parabolic Problems, Monograph in preparation, 2001. (2001)
- The ${H}^{\infty}$-calculus and sums of closed operators, Math. Ann (to appear). (to appear) MR1866491
- Fractional powers of operators, Pacific J. Math. 1 (1966), 285–346. (1966) Zbl0154.16104MR0201985
- Linear and Quasilinear Equations of Parabolic Type, vol. 23, Transl. Math. Monographs. Amer. Math. Soc., 1968. (1968) MR0241822
- On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429–452. (1990) MR1038710
- Fractional powers of coercively positive sums of operators, Soviet Math. Dokl. 16 (1975), 1638–1641. (1975) Zbl0333.47010MR0482314

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.