scholarly journals Nondivergence parabolic equations in weighted variable exponent spaces

2017 ◽  
Vol 370 (4) ◽  
pp. 2263-2298 ◽  
Author(s):  
Sun-Sig Byun ◽  
Mikyoung Lee ◽  
Jihoon Ok
Keyword(s):  
Parabolic Equations ◽  
Variable Exponent ◽  
Variable Exponent Spaces ◽  
Weighted Variable

The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces

2008 ◽  
Vol 15 (4) ◽  
pp. 683-712
Author(s):  
Vakhtang Kokilashvili ◽  
Stefan Samko
Keyword(s):  
Metric Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Metric Spaces ◽  
Doubling Measure ◽  
Lower Dimension ◽  
Variable Exponent Spaces ◽  
Muckenhoupt Class ◽  
Muckenhoupt Condition ◽  
Weighted Variable

Abstract We study the boundedness of the maximal operator in the weighted variable exponent spaces 𝐿𝑝(·)(𝑋, ϱ) on a doubling measure metric space 𝑋. When 𝑋 is bounded, the weight belongs to a version of a Muckenhoupt-type class, which is narrower than the expected Muckenhoupt condition for a variable exponent, but coincides with the usual Muckenhoupt class 𝐴𝑝 in the case of a constant 𝑝. For the bounded 𝑋 we also consider the class of weights of the form , where the functions 𝑤𝑘(𝑟) have finite upper and lower indices 𝑚(𝑤) and 𝑀(𝑤) satisfying the condition , where 𝔡𝔦𝔪(𝑋) is a version of lower dimension of the space 𝑋. In the case of unbounded 𝑋 we admit weights of the form . Some of the results are new even in the case of a constant 𝑝. We also deal with some new notions of upper and lower local dimensions of measure metric spaces.

Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces

2018 ◽  
Vol 111 (1) ◽  
pp. 43-68
Author(s):  
Sergey Shmarev ◽  
Jacson Simsen ◽  
Mariza Stefanello Simsen ◽  
Marcos Roberto T. Primo
Keyword(s):  
Asymptotic Behavior ◽  
Sobolev Spaces ◽  
Parabolic Equations ◽  
Weighted Variable
Sign in / Sign up

Export Citation Format

Share Document