Today, the general Institute seminar was held at the Institute of Mathematics and Mechanics of the Ministry of Science and Education of the Republic of Azerbaijan.  At the seminar head of the Department “Nonharmonic Analysis”, Corresponding Member of ANAS, doctor of physical and mathematical sciences, prof. Bilal Telman oglu  Bilalov  made  a  presentation on the topic  “ Fredholm  property of the Dirichl problem for an elliptic equation of the 2nd order in Grand Sobolev spaces”.

In the report, a regular elliptic equation of the 2m order, whose coefficients of the principal part are continuous in the region Ω⊂Rn with a sufficiently smooth boundary ∂Ω, is considered. Lp) (Ω), 1<p<+∞ in the Grand-Lebesgue space is considered. This space is not a separable space. For this reason, the space Lp) (Ω) is defined as a separable subspace Np) (Ω) where infinitely differentiable functions are dense. The grand Sobolev space Np)2m(Ω) of 2m order Sobolev differential functions generated by the subspace Nq) (Ω) was determined. Chowder-type estimation is proved for this equation up to the boundary. Using this estimate, an a priori estimate was obtained and the fredholmness of the elliptic equation of 2m order viewed in Np)2m(Ω) space was proved.

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