论文标题
与各向异性$ p $ - laplace非线性的hölder规律性有关Quasilarear抛物线方程式 - 公告
Hölder regularity for quasilinear parabolic equations with anisotropic $p$-Laplace nonlinearity -- Announcement
论文作者
论文摘要
我们宣布一些新的结果，以证明弱解决方案的hölder连续性对准抛物线方程，其原型采用$$ u_t的形式 - div（| \ nabla u |^{p -2} {p -2} \ nabla u）= 0 （| u_ {x_1} |^{p_1-2} u_ {x_1}，| u_ {x_2} |^{p_2-2} u_ {x_2}，\ ldots | u_ {x_n} $ 1 <\ {p_1，p_2，\ ldots，p_n \} <\ infty $。我们开发了一种新技术，该技术独立于E.Dibenedetto在退化的情况下（$ p \ geq 2 $）和e.dibenedetto和y.z.Chen开发的“固有缩放方法”，而在单数案例中（$ p \ p \ leq 2 $），而是使用新的和基本的线性程序来处理非线性。
We announce some new results for proving Hölder continuity of weak solutions to quasilinear parabolic equations whose prototype takes the form $$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.
