Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity

Yuzhou Fang1, Chao Zhang2
1School of Mathematics, Harbin Institute of Technology, Harbin, China
2School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, China

Tóm tắt

We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous degeneracy or/and singularity $$\begin{aligned} \partial _t u=[|D u|^q+a(x,t)|D u|^s]\left( \Delta u+(p-2)\left\langle D^2 u\frac{D u}{|D u|},\frac{D u}{|D u|}\right\rangle \right) , \end{aligned}$$ where $$1

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