Aibeche, Aissa and Chikouche, Wided and Nicaise, Serge:
$L^p$Regularity of Transmission Problems in Dihedral Domains
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 633-660, Unione Matematica Italiana (English)
pdf (552 Kb), djvu (237 Kb). | MR 2351535 | Zbl 1178.47005
Sunto
Consideriamo il problema di trasmissione per l'operatore di Laplace per un cilindro retto con dati in $L^p$. Applicando la teoria delle somme di operatori negli spazi di Banach, dimostriamo che la soluzione ammette una decomposizione in una parte regolare in $W^{2,p}$ e una parte singolare esplicita.
Referenze Bibliografiche
[1]
J. O. ADEYEYE,
Generation of analytic semi-groups in $L_p(\Omega)$ by the Laplace operator,
Bollettino UMI, Analisi Funzionale e Applicazioni, Serie VI, Vol.
IV-C, no. 1 (
1985), 113-128. |
MR 805208 |
Zbl 0597.35035[2]
S. AGMON,
On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems,
Comm. Pure Appl. Math.,
15 (
1962), 119-147. |
fulltext (doi) |
MR 147774 |
Zbl 0109.32701[4]
D. L. BURKHOLDER,
A geometrical characterisation of Banach spaces in which martingale difference sequences are unconditional,
Ann. Probab.,
9, (
1981), 997-1011. |
MR 632972 |
Zbl 0474.60036[5]
P. CLÉMENT -
P. GRISVARD,
Somme d'opérateurs et régularité $L^p$ dans les problémes aux limites,
C. R. Acad. Sci., Paris,
314 (
1992), 821-824. |
MR 1166054 |
Zbl 0773.47033[6]
R. R. COIFMAN -
G. WEISS,
Transference methods in analysis,
C.B.M.S. regional conference series in Math.,
31,
A.M.S., Providence, Rhode Island,
1977. |
MR 481928 |
Zbl 0371.43009[7]
S. COMPANATO,
Generation of analytic semi-groups by elliptic operators of second order in Hölder spaces,
Ann. Scuola Nor. Sup. Pisa,
8 (
1981), 495-512. |
fulltext EuDML |
MR 634859[8]
G. DA PRATO -
P. GRISVARD,
Somme d'opérateurs linéaires et équations différentielles opérationnelles,
J. Math. Pures Appl. IX Ser.,
54 (
1975). |
MR 442749 |
Zbl 0315.47009[10]
A. FAVINI -
R. LABBAS -
K. LEMRABET -
S. MAINGOT,
Study of the limit of transmission problems in a thin layer by the sum theory of linear operators,
Rev. Mat. Complut.,
18 (
2005), 143-176. |
fulltext EuDML |
MR 2135536 |
Zbl 1144.34357[12]
P. GRISVARD,
Elliptic problems in nonsmooth domains,
Monographs and Studies in Mathematics 24,
Pitman, Boston,
1985. |
MR 775683 |
Zbl 0695.35060[14]
P. GRISVARD,
Problèmes aux limites dans les polygones, Mode d'emploi.
EDF, Bulletin de la direction des études et des recherches, Série C, Mathématiques informatique,
1 (
1989), 21-59. |
MR 840970[15]
P. GRISVARD,
Singularities in boundary value problems,
Research notes in appl. Maths,
22,
Masson Springer-Verlag,
1992. |
MR 1173209 |
Zbl 0766.35001[16]
P. GRISVARD,
Singular behaviour of elliptic problems in non Hilbertian Sobolev spaces,
J. Math. Pures Appl.,
74 (
1995), 3-33. |
MR 1313613 |
Zbl 0854.35018[17]
B. HEINRICH -
S. NICAISE -
B. WEBER,
Elliptic interface problems in axisymmetric domains. Part I: Singular functions of non-tensorial type,
Math. Nachr,
186 (
1997), 147-165. |
fulltext (doi) |
MR 1461218 |
Zbl 0890.35035[18]
R. LABBAS -
M. MOUSSAOUI -
M. NAJMI,
Singular behavior of the Dirichlet problem in Hölder spaces of the solutions to the Dirichlet problem in a cone,
Rend. Ist. Mat. Univ. Trieste,
30 (
1998), 155-179. |
MR 1704849 |
Zbl 0952.35020[19]
C. MARTINEZ CARRACEDO -
M. SANZ ALIX,
The Theory of Fractional Powers of Operators, Saul Lubkin,
North-Holland,
2001. |
MR 1850825 |
Zbl 0971.47011[21]
S. NICAISE,
Polygonal interface problems,
Peter Lang, Berlin,
1993. |
MR 1236228[22]
A. PAZY,
Semigroups of linear operators and applications to partial differential equations,
Applied Math. Sciences,
44,
Springer-Verlag, New York,
1983. |
fulltext (doi) |
MR 710486 |
Zbl 0516.47023[23] P. E. SOBOLEVSKII, Equation of Parabolic type in Banach space, Amer. Math. Soc. Transl., 2 (1965), 1-62.
Con il contributo del Ministero per i Beni e le Attività Culturali