A priori estimates for very fast diffusion equations in ?n
Guy Bernard · Mathematical Methods in the Applied Sciences · 2000
A priori estimates are established for the very fast diffusion equation in \documentclass{article}\pagestyle{empty}\usepackage{amsfonts}\begin{document}\thispagestyle{empty}$\mathbb{R} \times (0,T)$\end{document} where in the form of necessary conditions on the initial value and the time level T. The demonstration is based on the volumetric mean of the solutions. Also, given are a priori estimates for the related elliptic equation in \documentclass{article}\pagestyle{empty}\usepackage{amsfonts}\begin{document}\thispagestyle{empty}$\mathbb{R}^n$\end{document} where and in the form of necessary conditions on the non-homogeneous term ƒ(x) and the parameter λ. Necessary conditions on the domain of the evolution operator follows from these results. Copyright © 2000 John Wiley & Sons, Ltd.