On Weighted Estimates of Solutions for Nonlinear Higher Order Elliptic Problems

Author: D'Asero S.  

Publisher: Taylor & Francis Ltd

ISSN: 0003-6811

Source: Applicable Analysis, Vol.82, Iss.1, 2003-01, pp. : 55-74

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Abstract

In the domain D = Omega - F it is considered a degenerate nonlinear higher order elliptic equation such that the corresponding energetic space is W1,q (D, wq) cap Wm,p (D, wp), mp < q < n, and wq, wp are weighted functions from some Muckenhoupt classes. A behavior of a solution u(x) is studied for the equation under consideration with the boundary value condition , where and f (x) = 1 for x isin F. The pointwise estimate for u(x) is proved in terms of the weighted higher order capacity of the set F and the distance from the point x to the set F.