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Existence of a Classical Solution for a Multidimensional Filtration Problem
Author(s) -
Gianni Roberto,
Mannucci Paola
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970125)20:2<179::aid-mma855>3.0.co;2-#
Subject(s) - mathematics , filtration (mathematics) , mathematical analysis , calculus (dental) , pure mathematics , medicine , dentistry
We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set { u =0}) of a multidimensional filtration problem. The key point to get the regularity of the level set { u =0} is the proof of an a priori estimate for the L ∞ ‐norm of u t . © 1997 by B.G. Teubner Stuttgart‐John Wiley & Sons, Ltd.