论文信息 - Good and viscosity solutions of fully nonlinear elliptic equations

Good and viscosity solutions of fully nonlinear elliptic equations

We introduce the notion of a good solution of a fully nonlinear uniformly elliptic equation. It is proven that good solutions are equivalent to L p -viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic equation and its L p -viscosity solution. The results also extend some results about good solutions of linear equations.

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