Geodesic
Quasiregular solutions for systems of hypoelliptic differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 25-31 
A. S. Kopets. Quasiregular solutions for systems of hypoelliptic differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a2/
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     title = {Quasiregular solutions for systems of~hypoelliptic differential equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The concept of a quasiregular solution is introduced for a special class of systems of linear partial differential equations of first order, considered on the space of continuously differentiable functions. The methods of distribution theory are used to prove the infinite differentiability of the components of quasiregular solutions of the considered systems, and integral representations of potential type are obtained for them. Examples of quasiregular solutions are given for systems of linear equations of elasticity theory.

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[2] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 2. Differentsialnye operatory s postoyannymi koeffitsientami, Mir, M., 1986 | MR

[3] Sedov L. I., Mekhanika sploshnoi sredy, T. I, Nauka, M., 1983 | MR

[4] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[5] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR | Zbl

[6] Shvarts L., Matematicheskie metody dlya fizicheskikh nauk, Mir, M., 1965 | MR

[7] Novatskii V., Teoriya uprugosti, Mir, M., 1975 | MR

[8] Kopets A. S., PMM, 52:6 (1988), 1013–1021 | MR | Zbl