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First order linear partial differential equations with discontinuous coefficients. (English) Zbl 0474.35081


MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35B65 Smoothness and regularity of solutions to PDEs
35F10 Initial value problems for linear first-order PDEs
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[1] Cambini, A.; Querci, S., Equazioni differenziali del primo ordine con secondo membro discontinuo rispetto all’incognita, Rend. Ist. Mat. Univ. Trieste, 1, 89-97 (1969) · Zbl 0193.04203
[2] Colombini, F., On the regularity of solutions of hyperbolic equations with discontinuous coefficients variable in time (1976), Pisa: Editrice Tecnico Scientifica, Pisa
[3] Colombini, F.; De Giorgi, E.; Spagnolo, S., Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. S.N.S. Pisa, Serie IV, 6, 3, 511-559 (1979) · Zbl 0417.35049
[4] Conway, E. D., Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws, Journ. Math. An. Appl., 18, 238-251 (1967) · Zbl 0163.12103
[5] De Simon, L.; Torelli, G., Linear second order differential equations with discontinuous coefficients in Hilbert spaces, Ann. S.N.S. Pisa, Serie IV, I, 1-2, 131-154 (1974) · Zbl 0318.35055
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[7] Hurd, A. E.; Sattinger, D. H., Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. A.M.S., 132, 159-174 (1968) · Zbl 0155.16401
[8] G.Malgarini,Su un particolare sistema differenziale ordinario con coefficienti discontinui, Ist. Lom. Acc. Scienze e Lett. (1960). · Zbl 0099.07103
[9] Pucci, A., Sistemi di equazioni differenziali con secondo membro discontinuo rispetto all’incognita, Rend. Ist. Mat. Univ. Trieste, 3, 75-80 (1971) · Zbl 0238.34008
[10] Pucci, A., Traiettorie di campi di vettori discontinui, Rend. Ist. Mat. Univ. Trieste, 8, 84-93 (1976) · Zbl 0343.57010
[11] Stampacchia, G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Four., 15, 1, 189-258 (1965) · Zbl 0151.15401
[12] K.Yosida,Functional analysis, Springer-Verlag (1966). · Zbl 0830.46001
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