Monotone operator theory for unsteady problems in variable exponent spaces
Monotone operator theory for unsteady problems in variable exponent spaces
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DOI：
10.1080/17476933.2011.557157
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发表时间：
2012-10
影响因子：
0.9
通讯作者：
L. Diening;P. Nägele;M. Růžička
中科院分区：
文献类型：
--
作者：
L. Diening;P. Nägele;M. Růžička
本文利用单调算子理论引入函数空间来处理变指数抛物型方程。推广了光滑函数的密度和分部积分公式等经典结果，证明了一类含p（τ，x）-结构椭圆算子的抛物型方程A弱解的存在性、唯一性和L2连续性，其中p是全局log-Hölder连续变量指数，满足1 < p − ≤ p + < ∞.
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 < p − ≤ p + < ∞.