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Principal curvature estimates for the convex level sets of semilinear elliptic equations

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  • We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary gradient. We also extend this result to a class of semi-linear elliptic partial differential equations under certain structure condition.
    Mathematics Subject Classification: 35J05, 53J67.

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