首页 | 本学科首页   官方微博 | 高级检索  
     


A Two-Phase Parabolic Free Boundary Problem with Coefficients Below the Lipschitz Threshold
Authors:Erik Lindgren  Jyotshana V. Prajapat
Affiliation:1. Department of Mathematical Sciences, NTNU, 7491, Trondheim, Norway
2. College of Arts & Sciences, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates
Abstract:We study the regularity of a parabolic free boundary problem of two-phase type with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the optimal ${C_x^{1,1}cap C_t^{0,1}}$ -regularity of the solution and that the free boundary is, near the so-called branching points, the union of two graphs that are Lipschitz in time and C 1 in space. In our case, the same monotonicity formula does not apply in the same way. Instead we use scaling arguments similar to the ones used for the elliptic case in Edquist et al. (Ann Inst Henri Poincareé, Anal Non Linéaire 26(6):2359?C2372, 2009) to prove the optimal regularity. However, whenever the spatial gradient does not vanish on the free boundary, we are in the parabolic setting faced with some extra difficulties, that forces us to strain our assumptions slightly.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号