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I work on Stochastic Control theory and BSDE's for my research. In my research, I characterized the set I am interested in as the level set of a function which is a viscosity solution to nonlinear PDE (HJB Equation). I was able to prove that this set is unbounded.(Its a 2 dimensional set)

$D(t,x) = \left\{(y_1,y_2) : w(t,x,y_1,y_2)=0 \right\}$ where $w$ is the solution to HJB equation.

Now, let $h(t,x,y_1) = \sup \left\{y_2 : w(t,x,y_1,y_2) = 0 \right\}$. Are there any techniques to characterize $h$ as solution to some PDE.

Thanks

chandu1729
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    I think that more people can help, if you just write down some details and equations that you mentioned in the question in a more comprehensive way! Doing this will soundly increase your chance of receiving good answers! :) – Hosein Rahnama Oct 25 '15 at 11:52

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