Banach空间中具有非自治扰动的发展方程的正则性
Regularity for evolution equations with non-autonomous perturbations in Banach spaces
摘要：
本文给出了Banach空间上一类发展方程解的正则性，其中生成元由一个静态主元和一个非自治扰动组成。正则性检查相对于主部分的迭代的图范数。将所得结果应用于薛定谔方程，得到了高阶Sobolev空间中含时标量势解正则性的条件.
英文摘要：
We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm of the iterations of the principal part. The results are applied to the Schrödinger equation and conditions on a time-dependent scalar potential for regularity of the solution in higher Sobolev spaces are derived.
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