Generation of Analytic Semigroups by Elliptic Operators with Unbounded Coefficients

1987 ◽  
Vol 18 (3) ◽  
pp. 857-872 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Elliptic Operators ◽  
Analytic Semigroups ◽  
Unbounded Coefficients

Generation of analytic semigroups in theL p topology by elliptic operators inR n

1988 ◽  
Vol 61 (3) ◽  
pp. 235-255 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Elliptic Operators ◽  
Analytic Semigroups

scholarly journals Generation results for vector-valued elliptic operators with unbounded coefficients in $$L^p$$ spaces

2021 ◽  
Author(s):  
Luciana Angiuli ◽  
Luca Lorenzi ◽  
Elisabetta M. Mangino ◽  
Abdelaziz Rhandi
Keyword(s):  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Elliptic Operators ◽  
Unbounded Coefficients ◽  
First Order ◽  
Vector Valued

AbstractWe 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.

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