paper and [22] we establish higher integrability and removability properties of solutions v: V →Rm, V ⊂ Rn, of the following inequality F(v(x)) KG( <...> author has proved the theorems ([19, Theorems 1 and 3–6]) on stability of the class of solutions to the equation F(u(x)) = G(u(x)) a. e. x ∈ V (3) (also see [16–18]). Our main results are analogs of the well-known higher integrability and removability loc (V ;Rn) of an open set V ⊂ Rn is an (se <...> ological, then v is K-quasiconformal. The distortion inequality is the particular case of (2) with the following functions F(v(x)) = |v(x)|n and G(v(x)) = det v(x). The theory of quasiconformal mappings and mappings with bounded distortion is the key part of modern geometric analysis which has <...> ined by inequality (4), i. e. v is a weakly quasire <...> may be smaller then the dimension n. In this case, det v(x) need not be locally integrable. Thus the natural exponent for the distortion inequality is the dimension n. K. Ast <...> from [19]. Let n,m,k ∈ N such that 2 k min{n,m}. We need the following hypothesis on Egorov A. A. Solutions of the differential inequality with a nu <...> A. 4. Proof of the Higher Intagrability Theorem is non-negative as otherwise we could consider |ϕ| which has <...>
Владикавказский_математический_журнал_№3_2014.pdf
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