Good and viscosity solutions of fully nonlinear elliptic equations

Jensen, Robert; Kocan, Maciej; Święch, Andrzej

doi:10.1090/S0002-9939-01-06115-9

Good and viscosity solutions of fully nonlinear elliptic equations
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by Robert Jensen, Maciej Kocan and Andrzej Święch PDF

Proc. Amer. Math. Soc. 130 (2002), 533-542 Request permission

Abstract:

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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