论文标题
不均匀的多孔介质方程的尖锐规律性
Sharp regularity for the inhomogeneous porous medium equation
论文作者
论文摘要
我们表明，不均匀的多孔介质方程的局部有限解决方案$$ u_ {t} - {\ rm div} \ left（m | \left\{ \frac{α_{0}^-}{m}, \frac{[(2q - n)r -2q]}{q[(mr - (m-1)]} \right\},$$ where $α_{0}$ denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation在适当的固有缩放中进行引理和几何迭代。
We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{t} - {\rm div} \left( m |u|^{m-1} \nabla u \right) = f \in L^{q,r}, \quad m >1 ,$$ are locally Hölder continuous, with exponent $$γ=\min \left\{ \frac{α_{0}^-}{m}, \frac{[(2q - n)r -2q]}{q[(mr - (m-1)]} \right\},$$ where $α_{0}$ denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.
