| Title:
|
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces (English) |
| Author:
|
Prüss, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
311-327 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
maximal regularity |
| Keyword:
|
sectorial operators |
| Keyword:
|
interpolation |
| Keyword:
|
trace theorems |
| Keyword:
|
elliptic and parabolic initial-boundary value problems |
| Keyword:
|
dynamic boundary conditions |
| MSC:
|
34G10 |
| MSC:
|
35G10 |
| MSC:
|
35K20 |
| MSC:
|
35K90 |
| MSC:
|
45K05 |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 1010.35064 |
| idMR:
|
MR1981536 |
| DOI:
|
10.21136/MB.2002.134160 |
| . |
| Date available:
|
2012-10-05T13:05:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134160 |
| . |
| Reference:
|
[1] G. Da Prato, P. Grisvard: Sommes d’opérateurs linéaires et équations différentielles opérationelles.J. Math. Pures Appl. 54 (1975), 305–387. MR 0442749 |
| Reference:
|
[2] G. Dore, A. Venni: On the closedness of the sum of two closed operators.Math. Z. 196 (1987), 189–201. MR 0910825, 10.1007/BF01163654 |
| Reference:
|
[3] J. Escher, J. Prüss, G. Simonett: Analytic solutions of the Stefan problem with Gibbs-Thomson correction.(to appear). |
| Reference:
|
[4] J. Escher, J. Prüss, G. Simonett: Analytic solutions of the free boundary value problem for the Navier-Stokes equation.(to appear). |
| Reference:
|
[5] P. Grisvard: Spaci di trace e applicazioni.Rend. Math. 5 (1972), 657–729. MR 0341059 |
| Reference:
|
[6] M. Hieber, J. Prüss: Maximal Regularity of Parabolic Problems.Monograph in preparation, 2001. |
| Reference:
|
[7] N. Kalton, L. Weis: The $H^\infty $-calculus and sums of closed operators.Math. Ann (to appear). MR 1866491 |
| Reference:
|
[8] H. Komatsu: Fractional powers of operators.Pacific J. Math. 1 (1966), 285–346. Zbl 0154.16104, MR 0201985 |
| Reference:
|
[9] O. A. Ladyženskaya, V. A. Solonnikov, N. N. Ural’ceva: Linear and Quasilinear Equations of Parabolic Type, vol. 23.Transl. Math. Monographs. Amer. Math. Soc., 1968. MR 0241822 |
| Reference:
|
[10] J. Prüss, H. Sohr: On operators with bounded imaginary powers in Banach spaces.Math. Z. 203 (1990), 429–452. MR 1038710, 10.1007/BF02570748 |
| Reference:
|
[11] P. E. Sobolevskii: Fractional powers of coercively positive sums of operators.Soviet Math. Dokl. 16 (1975), 1638–1641. Zbl 0333.47010, MR 0482314 |
| . |
