requirement of ellipticity property in definning viscosity solution

Question

Why it is important to require ellipticity condition in defining the notion of viscosity solution of degenerate elliptic or parabolic pde.

score 1 · Answer 1 · answered Jul 31 '13 at 15:31

1

Without ellipticity, you don't have a comparison principle, and the entire idea of viscosity solutions is to compare against suitable continuous functions.

answered Jul 31 '13 at 15:31

Ray Yang

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requirement of ellipticity property in definning viscosity solution

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