Geodesic
The Maximum Principle for Parabolic Inequalities on Stratified Sets
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 244-257

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In this paper, we consider the heat conduction operator with elliptic part of divergent type on a stratified set (i.e., on the set of manifolds of various dimension). We prove an analog of the lemma on the normal derivative and the weak and strong maximum principles for parabolic inequalities on this set. 
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     author = {V. V. Kulyaba and O. M. Penkin},
     title = {The {Maximum} {Principle} for {Parabolic} {Inequalities} on {Stratified} {Sets}},
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V. V. Kulyaba; O. M. Penkin. The Maximum Principle for Parabolic Inequalities on Stratified Sets. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 244-257. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a8/