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ROLLING STONES WITH NONCONVEX SIDES I: REGULARITY THEORY

  • Lee, Ki-Ahm ;
  • Rhee, Eun-Jai
  • Received : 2010.10.23
  • Published : 2012.03.01

Abstract

In this paper, we consider the regularity theory and the existence of smooth solution of a degenerate fully nonlinear equation describing the evolution of the rolling stones with nonconvex sides: $\{M(h)=h_t-F(t,z,z^{\alpha}h_{zz})\;in\;\{0<z{\leq}1\}{\times}[0,T] \\ h_t(z,t)=H(h_z(z,t),h)\;{on}\;\{z=0\}$. We establish the Schauder theory for $C^{2,{\alpha}}$-regularity of h.

Keywords

rolling stone;degenerate fully nonlinear equations;free boundary problem

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