论文标题
关于双线非线性方程的签名解决方案的赫德尔规律性
On the Hölder regularity of signed solutions to a doubly nonlinear equation
论文作者
论文摘要
我们建立了可能改变签名的解决方案的内部和边界连续性，这些解决方案可能会改变一类双线性抛物线方程，其原型为\ [\ partial_t \ big（| | u |^{p-2} u \ big）-Δ_Pu = 0，\ quad p> p> 1。 \]证明依赖于阳性的扩展和内在缩放的方法，所有这些都由de Giorgi的迭代实现。我们的方法同时强调了子（超级）溶液的不同作用，但足够灵活，可以在圆柱形域中获得迪里奇莱特类型或neumann型的初始有限价值问题的hölder规律性，直到抛物线范围。此外，基于阳性的扩大，我们能够为Harnack对非负解决方案的不平等做出替代证明。此外，由于内部估计，我们还获得了liouville型的结果。
We establish the interior and boundary Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{p-2}u\big)-Δ_p u=0,\quad p>1. \] The proof relies on the property of expansion of positivity and the method of intrinsic scaling, all of which are realized by De Giorgi's iteration. Our approach, while emphasizing the distinct roles of sub(super)-solutions, is flexible enough to obtain the Hölder regularity of solutions to initial-boundary value problems of Dirichlet type or Neumann type in a cylindrical domain, up to the parabolic boundary. In addition, based on the expansion of positivity, we are able to give an alternative proof of Harnack's inequality for non-negative solutions. Moreover, as a consequence of the interior estimates, we also obtain a Liouville-type result.
