Optimal Gradient Estimates for Parabolic Equations in Variable Exponent Spaces

2015 ◽  
Vol 2016 (8) ◽  
pp. 2493-2521 ◽  
Author(s):  
Sun-Sig Byun ◽  
Jihoon Ok
Keyword(s):  
Parabolic Equations ◽  
Variable Exponent ◽  
Gradient Estimates ◽  
Variable Exponent Spaces

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

GRADIENT ESTIMATES VIA TWO-POINT FUNCTIONS FOR PARABOLIC EQUATIONS UNDER RICCI FLOW

2020 ◽  
Vol 102 (2) ◽  
pp. 319-330
Author(s):  
MIN CHEN
Keyword(s):  
Riemannian Manifolds ◽  
Ricci Flow ◽  
Parabolic Equations ◽  
Gradient Estimates ◽  
Quasilinear Parabolic Equations ◽  
Quasilinear Parabolic

We derive estimates relating the values of a solution at any two points to the distance between the points for quasilinear parabolic equations on compact Riemannian manifolds under Ricci flow.

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