Elliptic operators with unbounded coefficients: construction of a maximal dissipative extension

2001 ◽  
Vol 1 (1) ◽  
pp. 1-18 ◽  
Author(s):  
G. Da Prato
Keyword(s):  
Elliptic Operators ◽  
Unbounded Coefficients ◽  
Dissipative Extension

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.

scholarly journals Elliptic Operators on Rd with Unbounded Coefficients

2001 ◽  
Vol 172 (2) ◽  
pp. 333-358 ◽  
Author(s):  
Giuseppe Da Prato ◽  
Beniamin Goldys
Keyword(s):  
Elliptic Operators ◽  
Unbounded Coefficients

Uniqueness for elliptic operators on with unbounded coefficients

2010 ◽  
Vol 22 (3) ◽  
Author(s):  
Giorgio Metafune ◽  
Diego Pallara ◽  
Patrick J. Rabier ◽  
Roland Schnaubelt
Keyword(s):  
Elliptic Operators ◽  
Unbounded Coefficients

scholarly journals Lp-uniqueness for elliptic operators with unbounded coefficients in RN

2009 ◽  
Vol 256 (4) ◽  
pp. 1238-1257 ◽  
Author(s):  
Angela Albanese ◽  
Luca Lorenzi ◽  
Elisabetta Mangino
Keyword(s):  
Elliptic Operators ◽  
Unbounded Coefficients
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