具有各向异性$p$ -Laplace非线性项的拟线性抛物型方程的Hölder正则性
Hölder regularity for quasilinear parabolic equations with anisotropic $p$-Laplace nonlinearity -- Announcement
摘要：
本文给出了拟线性抛物型方程弱解的Hölder连续性的一些新结果，其原型为$$u_t - div (|\nabla u|^{p-2}\nabla u)= 0 \qquad \text{or} \qquad u_t - div (|u_{x_1}|^{p_1-2}u_{x_1},|u_{x_2}|^{p_2-2}u_{x_2},\ldots |u_{x_N}|^{p_N-2}u_{x_N})=0$$和$1<\{p_1,p_2,\ldots,p_N\}<\infty$ .我们开发了一种新的技术，这是独立的“方法的内在标度”开发的E.DiBenedetto在退化的情况下（$p\geq 2$）和E.DiBenedetto和Y. Z.陈在奇异的情况下（$p\leq 2$），而是使用一个新的和基本的线性化过程来处理的非线性。
英文摘要：
We announce some new results for proving Hölder continuity of weak solutions to quasilinear parabolic equations whose prototype takes the form $$u_t - div (|\nabla u|^{p-2}\nabla u)= 0 \qquad \text{or} \qquad u_t - div (|u_{x_1}|^{p_1-2}u_{x_1},|u_{x_2}|^{p_2-2}u_{x_2},\ldots |u_{x_N}|^{p_N-2}u_{x_N})=0$$ and $1<\{p_1,p_2,\ldots,p_N\}<\infty$. We develop a new technique which is independent of the "method of intrinsic scaling" developed by E.DiBenedetto in the degenerate case ($p\geq 2$) and E.DiBenedetto and Y.Z.Chen in the singular case ($p\leq 2$) and instead uses a new and elementary linearisation procedure to handle the nonlinearity.
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