论文标题
伪单酮操作员理论，用于可变指数空间中的不稳定问题
Pseudo-monotone operator theory for unsteady problems in variable exponent spaces
论文作者
论文摘要
我们通过高级伪单调方法证明了抛物线偏微分方程的抽象存在结果，其$ \ log $-Hölder连续可变指数非线性仅由梯度的对称部分控制。为此，我们介绍了Bochner伪单调性和Bochner的强制性，这是对可变指数空间中伪单调性和对不稳定问题的概念的适当扩展。在这种情况下，我们采用了所谓的Hirano-Landes方法，这使我们能够为这些新概念提供一般且易于证实的条件。此外，我们证明仅涉及梯度的对称部分的必需抛物面嵌入和紧凑性结果。
We prove by means of advanced pseudo-monotonicity methods an abstract existence result for parabolic partial differential equations with $\log$-Hölder continuous variable exponent nonlinearity governed by the symmetric part of a gradient only. To this end, we introduce the notions Bochner pseudo-monotonicity and Bochner coercivity, which are appropriate extensions of the concepts of pseudo-monotonicity and coercivity to unsteady problems in variable exponent spaces. In this context, we apply the so-called Hirano-Landes approach, which enables us to give general and easily verifiable conditions for these new notions. Moreover, we prove essential parabolic embedding and compactness results involving only the symmetric part of the gradient.
