All the generalized characteristics for the solution to a Hamilton–Jacobi equation with the initial data of the Takagi function

Yasuhiro Fujita (), Nao Hamamuki () and Norikazu Yamaguchi ()
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Yasuhiro Fujita: University of Toyama
Nao Hamamuki: Hokkaido University
Norikazu Yamaguchi: University of Toyama

Partial Differential Equations and Applications, 2020, vol. 1, issue 6, 1-20

Abstract: Abstract We determine all the generalized characteristics for the solution to a Hamilton–Jacobi equation with the initial data of the Takagi function, which is everywhere continuous and nowhere differentiable. This result clarifies how singularities of the solution propagate along generalized characteristics. Moreover it turns out that the Takagi function still keeps the validity of the recent results in Albano et al. (J. Differ. Equ. 268:1412–1426, 2020), in which locally Lipschitz continuous initial data are handled.

Keywords: The Takagi function; Propagation of singularities; Generalized characteristics; Primary 35F21; 35A21; Secondary 26A27 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00039-7

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