Existenz einer schwachen Lösung eines entarteten parabolischen Rand- Anfangswertproblems zwischen schwachen Ober- und Unterlösungen (Q790357)

Supposing that there is a smooth weak upper and lower solution of the problem \[ u'-div_ x(| u|^{p-2}\text{grad}_ xu)=0\quad in\quad G\times(0,T),\quad u|_{\partial G\times(0,T)}=0,\quad u(x,0)=u_ 0(x),\quad x\in G, \] the author shows the existence of a weak solution lying between the upper and lower solution. Concerning the general existence theory of weak solutions to this degenerate parabolic problem cf. \textit{J. L. Lions} [Quelques méthodes de résolution des problèmes aux limites non linéaires (1969; Zbl 0189.406) pp. 192].