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First eigenfunctions of the 1-Laplacian are viscosity solutions

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  • We address the question if eigenfunctions of the 1-Laplacian, which are obtained through a variational argument, are also viscosity solutions of the associated strongly degenerate formal Euler equation. The answer is positive, but examples show also that there are many more viscosity solutions than expected.
    Mathematics Subject Classification: Primary: 35D40, 35J70, 49G05, 49A52.


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