Geodesic
Classical solution of a degenerate elliptic-parabolic free boundary problem
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2011), pp. 295-332

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A free boundary problem describing a filtration process in a porous medium is considered. An unknown interface divides the filtration domain into elliptic and parabolic regions. In the parabolic region the governing equation is degenerate. The existence of a smooth solution in the weighted Hölder space is proved 
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     author = {B. V. Bazaliy and S. P. Degtyarev},
     title = {Classical solution of a degenerate elliptic-parabolic free boundary problem},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {295--332},
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     volume = {7},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2011_7_a0/}
}
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B. V. Bazaliy; S. P. Degtyarev. Classical solution of a degenerate elliptic-parabolic free boundary problem. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2011), pp. 295-332. http://geodesic.mathdoc.fr/item/JMAG_2011_7_a0/