Local Maximum Principle of Semilinear Nonuniformly Elliptic Equations and Its Applications to Hessian Equations
Jiguang Bao · Advances in Mathematics · 2004
We obtain a local maximum principle for the semilinear nonuniformly elliptic equations in divergence form, and then show the local C1'1 estimate and a Bernstein type result for the solutions of the Hessian equations.