Second order linear parabolic equations in uniform spaces in $${\varvec{\mathbb {R}^{N}}}$$ R N

2016 ◽  
Vol 30 (1) ◽  
pp. 63-78
Author(s):  
Carlos Quesada ◽  
Aníbal Rodríguez-Bernal
Keyword(s):  
Parabolic Equations ◽  
Second Order ◽  
Uniform Spaces ◽  
Order Linear ◽  
Linear Parabolic Equations

LINEAR PARABOLIC EQUATIONS IN LOCALLY UNIFORM SPACES

2004 ◽  
Vol 14 (02) ◽  
pp. 253-293 ◽  
Author(s):  
JOSE M. ARRIETA ◽  
ANIBAL RODRIGUEZ-BERNAL ◽  
JAN W. CHOLEWA ◽  
TOMASZ DLOTKO
Keyword(s):  
Linear Theory ◽  
Exponential Type ◽  
Parabolic Equations ◽  
Elliptic Operators ◽  
Second Order ◽  
Uniform Spaces ◽  
Linear Parabolic Equations ◽  
Second Order Elliptic Operators

We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp Lp-Lq-type estimates in uniform spaces for heat and Schrödinger semigroups and analyze the regularizing effect and the exponential type of these semigroups. We also deal with general second-order elliptic operators and study the generation of analytic semigoups in uniform spaces.

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