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We will prove a partial regularity result for the zero level set of weak solutions to where B = B(μ) = I + (A - I)χ{μ<0}, where I is the identity matrix and the eigenvalues of A are strictly positive and bounded. We will apply this to describe the regularity of solutions to the Bellman equations. © 2012 American Mathematical Society.

The zero level set for a certain weak solution, with applications to the Bellman equations