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Example of an \(\infty\)-harmonic function which is not \(C^2\) on a dense subset. (English) Zbl 1129.35421

Summary: We show that for certain boundary values, McShane-Whitney’s minimal-extension-like function is \(\infty\)-harmonic near the boundary and is not \(C2\) on a dense subset.

MSC:

35J70 Degenerate elliptic equations
26B05 Continuity and differentiation questions
35B65 Smoothness and regularity of solutions to PDEs
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