most recent 30 from http://mathoverflow.net 2013-05-26T04:14:07Z http://mathoverflow.net/feeds/question/26242 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/26242/regularity-of-2nd-order-parabolic-equation unknown (google) 2010-05-28T08:55:09Z 2010-05-28T14:23:37Z

<p>How can I show that the solution $V(t,S)$ in the following 2nd-order parabolic equation is in $C^{1,2}$ i.e. V(t,S) is continuous in time and 2nd continuous in S? </p> <p>$\begin{equation} \frac{\partial V(t,S)}{\partial t} + \frac{1}{2}\sigma^2 S^2\frac{\partial^2 V(t,S)}{\partial S^2}+rS\frac{\partial V(t,S)}{\partial S}-rV(t,S)=-\rho \max (G-V,0) \end{equation}$</p> <p>where $\sigma,r$ are real known constants and G$\equiv$G(S):=S-K where K is a positive real constant.</p>