2017
Том 69
№ 9

All Issues

Pointwise estimates of potentials for higher-order capacities

Skrypnik I. V.

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Abstract

In a domain D=Ω\ER n , we consider a nonlinear higher-order elliptic equation such that the corresponding energy space is W p m (D)W q 1 (D), q>mp, and estimate a solution u(x) of this equation satisfying the condition u(x)−kf(x)W p m (D)W q 1 (D), where kR 1, f(x)C 0 (Ω), and f(x)=1 for xF. We establish a pointwise estimate for u(x) in terms of the higher-order capacity of the set F and the distance from the point x to the set F.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 1, pp 165-180.

Citation Example: Skrypnik I. V. Pointwise estimates of potentials for higher-order capacities // Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 149–163.

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