Pointwise estimates of potentials for higher-order capacities

  • I. V. Skrypnik

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.
Published
25.01.1997
How to Cite
SkrypnikI. V. “Pointwise Estimates of Potentials for Higher-Order Capacities”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 1, Jan. 1997, pp. 149–163, https://umj.imath.kiev.ua/index.php/umj/article/view/4993.
Section
Research articles