Geodesic
The maximum principle for terminal optimization problem connected with Goursat--Darboux system in the class of functions having summable mixed derivatives
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 52-67

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The maximum principle in the terminal optimization problem for general nonlinear Goursat–Darboux system is proved. The right part of differential equation is Caratheodory function. We consider the case when a mixed derivative of system solution is summable function.
Keywords: nonlinear Goursat–Darboux system, solutions having summable mixed derivatives, terminal optimization problem, maximum principle. 
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     author = {I. V. Lisachenko and V. I. Sumin},
     title = {The maximum principle for terminal optimization problem connected with {Goursat--Darboux} system in the class of functions having summable mixed derivatives},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {52--67},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_2_a3/}
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I. V. Lisachenko; V. I. Sumin. The maximum principle for terminal optimization problem connected with Goursat--Darboux system in the class of functions having summable mixed derivatives. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 52-67. http://geodesic.mathdoc.fr/item/VUU_2011_2_a3/