Optimal second-order regularity in the space variables is established for solutions to Cauchy–Dirichlet problems for nonlinear parabolic equations and systems of p-Laplacian type, with square-integrable right-hand sides and initial data in a Sobolev space. As a consequence, generalized solutions are shown to be strong solutions. Minimal regularity on the boundary of the domain is required, though the results are new even for smooth domains. In particular, they hold in arbitrary bounded convex domains.

中文翻译：

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抛物线p -Laplace问题的二阶正则性

建立了空间变量的最佳二阶规​​则性，用于求解非线性抛物方程和p -Laplacian型系统的Cauchy-Dirichlet问题，并具有正方形可积分的右手边和Sobolev空间中的初始数据。结果，广义解被证明是强解。尽管结果对于平滑域也是新的，但仍要求在域边界上的规则性最小。特别地，它们保持在任意有界凸域中。