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.
EXISTENCE OF A CLASSICAL SOLUTION FOR A MULTIDIMENSIONAL FILTRATION PROBLEM / GIANNI, ROBERTO. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 20:(1997), pp. 179-187. [10.1002/(SICI)1099-1476(19970125)20:2<179::AID-MMA855>3.0.CO;2-#]
EXISTENCE OF A CLASSICAL SOLUTION FOR A MULTIDIMENSIONAL FILTRATION PROBLEM
GIANNI, ROBERTO
1997
Abstract
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.
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