On  June 21, 2023, 10.00 a.m., in the weekly Wednesday seminar the chair of the Department of “Non-harmonic analysis”  prof.  Bilal Telman oglu Bilalov  will give a talk on the topic ” Fredholmness of the Dirichlet problem for 2m-th order elliptic equations in grand Sobolev spaces”.

In the report  the 2m-th order uniformly elliptic equation whose coefficients of the principal part are continuous is considered on a bounded domain Ω⊂Rⁿ with sufficiently smooth boundary ∂Ω. Grand Lebesgue space L_p) (Ω), 1<p<+∞, is considered. This space is nonseparable and it is defined the separable subspace N_p) (Ω)  of L_p) (Ω) in which infinitely differentiable functions are dense. It is defined the grand Sobolev space N_p)^2m(Ω) of 2m-th order differentiable in Sobolev sense functions generated by subspace N_q) (Ω). The Schauder type estimate up to the boundary is proved for this equation. Using this estimate it is established the apriori estimate and then the Fredholmness of the considered 2m-th order elliptic equation in N_p)^2m(Ω). By solution we mean a strong solution.

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