标题： 关于带符号解的双重非线性方程的Hölder正则性。 第二部分 显示英文标题

标题： On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II

摘要： 我们展示了两种证明方法，用于证明一类双非线性抛物方程可能变号解的局部Hölder连续性，其典型例子是\[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad p>2,\quad 0<q<p-1. \]。第一个证明利用了退化抛物方程$p$-Laplacian的正性扩张，从而简化了论证；而另一个证明则仅依赖于双非线性抛物方程的能量估计。 在对内部论证进行适当调整后，我们也得到了Dirichlet型和Neumann型初边值问题的边界正则性。 显示英文摘要

摘要： We demonstrate two proofs for the local H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad p>2,\quad 0<q<p-1. \] The first proof takes advantage of the expansion of positivity for the degenerate, parabolic $p$-Laplacian, thus simplifying the argument; whereas the other proof relies solely on the energy estimates for the doubly nonlinear parabolic equations. After proper adaptions of the interior arguments, we also obtain the boundary regularity for initial-boundary value problems of Dirichlet type and Neumann type.