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 $D^{1,1}$, $D^{1,0}$, $D^{0,1}$ 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/