Generation results for vector-valued elliptic operators with unbounded coefficients in $$L^p$$ spaces
Abstract We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space $$L^p({\mathbb {R}}^d;{\mathbb {R}}^m)$$ L p ( R d ; R m ) with $$p \in (1,\infty )$$ p ∈ ( 1 , ∞ ) . Sufficient conditions to prove generation results o...
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| Published in | Annali di matematica pura ed applicata Vol. 201; no. 3; pp. 1347 - 1379 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
01.06.2022
|
| Online Access | Get full text |
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| Summary: | Abstract
We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space
$$L^p({\mathbb {R}}^d;{\mathbb {R}}^m)$$
L
p
(
R
d
;
R
m
)
with
$$p \in (1,\infty )$$
p
∈
(
1
,
∞
)
. Sufficient conditions to prove generation results of an analytic
$$C_0$$
C
0
-semigroup
$${\varvec{T}}(t)$$
T
(
t
)
, together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established. |
|---|---|
| ISSN: | 0373-3114 1618-1891 |
| DOI: | 10.1007/s10231-021-01160-z |