ðə lˈɛbɛsɡ spˈaɪn wʌz ˌɪntɹədˈuːst ɪn nˈaɪntiːnhˈʌndɹɪd twˈɛlv baɪ hˈɛnɹi lˈɛbɛsɡ tə dˈɛmənstɹˌeɪt ðætðə dˈɪɹɪtʃlɪt pɹˈɑːbləm dʌznˌɑːt ˈɔːlweɪz hæv ɐ səlˈuːʃən, pɚtˈɪkjʊlɚli wɛn ðə bˈaʊndɚɹi hɐz ɐ səfˈɪʃəntli ʃˈɑːɹp ˈɛdʒ pɹətɹˈuːdɪŋ ˌɪntʊ ðɪ ɪntˈɪɹiɚɹ ʌvðə ɹˈiːdʒən.
The Lebesgue spine was introduced in 1912 by Henri Lebesgue to demonstrate that the Dirichlet problem does not always have a solution, particularly when the boundary has a sufficiently sharp edge protruding into the interior of the region.