Monotone operator theory for unsteady problems in variable exponent spaces

We introduce function spaces for the treatment of parabolic equations with variable exponents by means of the theory of monotone operators. We generalize classical results such as density of smooth functions and a formula for integration by parts to prove existence, uniqueness and L 2 -continuity of...

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Published in:Complex variables and elliptic equations 2012-11, Vol.57 (11), p.1209-1231
Main Authors: Diening, L., Nägele, P., Růžička, M.
Format: Article
Language:English
Subjects:
Complex variables
Density
Exponents
Function space
Mathematical analysis
monotone operator
Operators
Theory
Uniqueness
Unsteady
variable exponent spaces
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description We introduce function spaces for the treatment of parabolic equations with variable exponents by means of the theory of monotone operators. We generalize classical results such as density of smooth functions and a formula for integration by parts to prove existence, uniqueness and L 2 -continuity of weak solutions to parabolic equations involving elliptic operators A with p(τ, x)-structure, where p is a globally log-Hölder continuous variable exponent satisfying 1 
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subjects Complex variables
Density
Exponents
Function space
Mathematical analysis
monotone operator
Operators
Theory
Uniqueness
Unsteady
variable exponent spaces
title Monotone operator theory for unsteady problems in variable exponent spaces
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