At critical points of solutions to linear elliptic equations, the second (resp. third) derivative now provably exists under sharp DMO coefficient assumptions, refining Teixeira's C^{1,1-} regularity to a C^{1,α}-type pointwise estimate.
Potential Anal.52(2022), no
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Refined regularity at critical points for linear elliptic equations
At critical points of solutions to linear elliptic equations, the second (resp. third) derivative now provably exists under sharp DMO coefficient assumptions, refining Teixeira's C^{1,1-} regularity to a C^{1,α}-type pointwise estimate.