Geodesic
On the maximum principle for solutions of second order elliptic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 11-17

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In this paper the sufficient conditions, under which the maximum princirle for the solution of second order partial differential elliptic equation in the unit circle meets maximum princirle are researched. It is proved that if a quasiconformality coefficient of such function satisfies certain boundary conditions then this function meets maximum principle. Proving the main result we use integral representations of solutions of this equation and properties of Cauchy type integral and functions of Hardy and Smirnoff classes.
Mots-clés : elliptic equation, quasiconformality coefficient.
Keywords: maximum principle 
@article{IVM_2020_8_a1,
     author = {A. B. Zaitsev},
     title = {On the maximum principle for solutions of second order elliptic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--17},
     publisher = {mathdoc},
     number = {8},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_8_a1/}
}
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A. B. Zaitsev. On the maximum principle for solutions of second order elliptic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 11-17. http://geodesic.mathdoc.fr/item/IVM_2020_8_a1/