Geodesic
Partial differential equations in Banach spaces involving nilpotent linear operators
Annales Polonici Mathematici, Tome 65 (1996) no. 1, pp. 67-80

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let E be a Banach space. We consider a Cauchy problem of the type ⎧ $D^{k}_{t}u + ∑_{j=0}^{k-1}∑_{|α|≤m} A_{j,α}(D^{j}_{t} D^{α}_{x}u) = f$ in $ℝ^{n+1}$, ⎨ ⎩ $D^{j}_{t} u(0,x) = φ_j(x)$ in $ℝ^n$, j=0,...,k-1, where each $A_{j,α}$ is a given continuous linear operator from E into itself. We prove that if the operators $A_{j,α}$ are nilpotent and pairwise commuting, then the problem is well-posed in the space of all functions $u ∈ C^∞(ℝ^{n+1},E)$ whose derivatives are equi-bounded on each bounded subset of $ℝ^{n+1}$.
DOI : 10.4064/ap-65-1-67-80
Keywords: partial differential equations in Banach spaces, nilpotent operators

Antonia Chinnì 1 ; Paolo Cubiotti 1

1 
@article{10_4064_ap_65_1_67_80,
     author = {Antonia Chinn{\`\i} and Paolo Cubiotti},
     title = {Partial differential equations in {Banach} spaces involving nilpotent linear operators},
     journal = {Annales Polonici Mathematici},
     pages = {67--80},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {1996},
     doi = {10.4064/ap-65-1-67-80},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-65-1-67-80/}
}
TY  - JOUR
AU  - Antonia Chinnì
AU  - Paolo Cubiotti
TI  - Partial differential equations in Banach spaces involving nilpotent linear operators
JO  - Annales Polonici Mathematici
PY  - 1996
SP  - 67
EP  - 80
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-65-1-67-80/
DO  - 10.4064/ap-65-1-67-80
LA  - en
ID  - 10_4064_ap_65_1_67_80
ER  - 
%0 Journal Article
%A Antonia Chinnì
%A Paolo Cubiotti
%T Partial differential equations in Banach spaces involving nilpotent linear operators
%J Annales Polonici Mathematici
%D 1996
%P 67-80
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-65-1-67-80/
%R 10.4064/ap-65-1-67-80
%G en
%F 10_4064_ap_65_1_67_80
Antonia Chinnì; Paolo Cubiotti. Partial differential equations in Banach spaces involving nilpotent linear operators. Annales Polonici Mathematici, Tome 65 (1996) no. 1, pp. 67-80. doi: 10.4064/ap-65-1-67-80

Cité par Sources :