Geodesic
On the structure of the solution of the Hamilton-Jacobi equation with piecewise linear input data
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 144-147

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The Cauchy problem is considered for the Hamilton Jacobi equation with Hamiltonian depending on the impulse variable only. Estimations have been obtained for the minimax (and/or viscosity) solution to this problem in the case of piecewise linearity of the Hamiltonian or the border function. The proposed estimations provide explicit formulas for the minimax solution, if «minimaxes» and «maximins» contained in them coincide. 
@article{VUU_2008_2_a47,
     author = {N. N. Subbotina and L. G. Shagalova},
     title = {On the structure of the solution of the {Hamilton-Jacobi} equation with piecewise linear input data},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {144--147},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2008_2_a47/}
}
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N. N. Subbotina; L. G. Shagalova. On the structure of the solution of the Hamilton-Jacobi equation with piecewise linear input data. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2008), pp. 144-147. http://geodesic.mathdoc.fr/item/VUU_2008_2_a47/