Lp-estimates for parabolic systems with unbounded coefficients coupled at zero and first order

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space Lp(Rd;Rm)(d,m≥1) with p∈[1,+∞). Sufficient conditions for the associated evolution operator G(t,s) in Cb(Rd;Rm) to extend to a strongly continuous operator in Lp(Rd;Rm) are given. Some Lp–Lq estimates ar...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 444; no. 1; pp. 110 - 135
Main Authors Angiuli, Luciana, Lorenzi, Luca, Pallara, Diego
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2016
Subjects
[formula omitted]-estimates
Parabolic systems
Pointwise gradient estimates
Unbounded coefficients
Lp-estimates
Parabolic systems
Unbounded coefficients
Pointwise gradient estimates
Online AccessGet full text

Cover

More Information
Summary:We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space Lp(Rd;Rm)(d,m≥1) with p∈[1,+∞). Sufficient conditions for the associated evolution operator G(t,s) in Cb(Rd;Rm) to extend to a strongly continuous operator in Lp(Rd;Rm) are given. Some Lp–Lq estimates are also established together with Lp gradient estimates.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.06.001