tes the differential of v at x ∈ V . Using the higher integrability theorem of the previous paper [8], we establish a result on removability of singularities for solutions to (1). farmal mappings and mappings with bounded distortion (for example, see [1, 2, 4], [9 <...> –[29] and the bibliography therein). Painlev´ Many investigations have dealt with the problem of removable singularities for quasicone’s theorem, a classical result in complex function theory, states that sets of zero length are removab <...> h the class of holomrphic functions. The strongest removability conjecture, stated in [14] as the counterpart of Painlev´ e’s theorem for mappings with bounded distortion, suggests that sets of Hausdorff α-measure zero, α n/(K + 1) n/2, are removable for bounded mapp <...> 2] for α = 2/(K + 1) (also see [3]). The higher integrability results for mappings with bounded distortion are closely <...> elated to the removability problems. Caccioppoli-type estimates (one of the key ingredients in proofs of higher integrability results) can be used as the basic to <...> variables (for example, see [5, 6]). Mappings of these classes, as mappings with bounded distortion, can be considered as solutions to (1) with specific functions F, G, and H. Our removability result (Theorem 1.1) contain partially the known results on removability of singula <...> ities for mappings of these classes. In this paper, using the Hodge decomposition theory developed by T. Iwaniec and G. Martin [13, 14, 15], we also obtain integral estimates for wedge products of closed differential forms (Theorem 2.3) and for minor <...> of a Jacobian matrix (Theorem 2.1). These estimates are extensions o <...> singularities for solutions to (1). We derive integral estimates for wedge products of closed differential forms and fo <...> n{n,m}, and let V be a domain in Rn. Suppose that a continuous function F : RmЧn →R satisfies (2 <...> the exponent from [8, Theorem 2.1]. For a closed subset E of V with the Hausdorff dimension dimH(E) < n−p every bounded solution v ∈W1,k of the class W1,k with some constant cF > 0, a null Lagrangian G: RmЧn → R is homogeneous of degree k, and a measurable function H: V →R has H+ ∈ Lt loc (V ;Rm) which is defined over the w <...> V ))j∈N such <...>
Владикавказский_математический_журнал_№4_2014.pdf
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