[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2012.49.2.265

ROLLING STONES WITH NONCONVEX SIDES I: REGULARITY THEORY

Lee, Ki-Ahm (Department of Mathematics Seoul National University)
Rhee, Eun-Jai (Department of Mathematics Seoul National University)

Publication Information

Journal of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 265-291 More about this Journal

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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