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

Andersson, J.; Mikayelyan, H.

doi:10.1090/S0002-9947-2012-05593-0

The zero level set for a certain weak solution, with applications to the Bellman equations
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by J. Andersson and H. Mikayelyan PDF

Trans. Amer. Math. Soc. 365 (2013), 2297-2316 Request permission

Abstract:

We will prove a partial regularity result for the zero level set of weak solutions to \[ \textrm {div}(B\nabla u)=0, \] where $B=B(u)=I+(A-I)\chi _{\{u<0\}}$, 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.

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