Geodesic
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 145-171.

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We give characterizations of the distributional derivatives D1,1, D1,0, D0,1 of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Classification : 26A21, 26A99, 26B05, 26B30, 35L10, 35R10, 46F10, 46G05 
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     title = {Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation},
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Idczak, Dariusz. Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 145-171. https://geodesic-test.mathdoc.fr/item/CMJ_1998__48_1_a12/