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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract: In this talk, we present a proof of  $$C^{1, \alpha}$$ regularity up to the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. The proof is achieved via compactness arguments combined with new boundary H\"{o}lder estimates for equations which are uniformly elliptic when the gradient is either small or large.