Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles
Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles
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DOI：
10.1007/s00229-014-0684-8
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发表时间：
2014-06
影响因子：
0.6
通讯作者：
Christoph Scheven
中科院分区：
文献类型：
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作者：
Christoph Scheven
我们引入了具有高度不规则障碍物的p-拉普拉斯型抛物线障碍问题的可局部解的概念，并给出了相应的存在性结果。构造的解决方案的主要新特征是它们在局部解决问题，这是检查正则性等局部属性的适当概念。作为一个应用，我们推导了抛物线障碍问题的可局部解的空间梯度的 Calderón-Zygmund 估计。
We introduce the concept of localizable solutions of parabolic obstacle problems ofp-Laplace-type with highly irregular obstacles and provide corresponding existence results. The main new feature of the constructed solutions is that they solve the problem locally, which is the appropriate notion for the examination of local properties like regularity. As an application, we derive Calderón–Zygmund estimates for the spatial gradient of localizable solutions to parabolic obstacle problems.