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On weighted estimates of solutions of nonlinear elliptic problems

Igor V. SkrypnikDmitry V. Larin — 1999

Mathematica Bohemica

The paper is devoted to the estimate u(x,k)Kk{capp,w(F)pw(B(x,))} 1p-1, 2 p < n for a solution of a degenerate nonlinear elliptic equation in a domain B ( x 0 , 1 ) F , F B ( x 0 , d ) = { x n | x 0 - x | < d } , d < 1 2 , under the boundary-value conditions u ( x , k ) = k for x F , u ( x , k ) = 0 for x B ( x 0 , 1 ) and where 0 < ρ d i s t ( x , F ) , w ( x ) is a weighted function from some Muckenhoupt class, and c a p p , w ( F ) , w ( B ( x , ρ ) ) are weighted capacity and measure of the corresponding sets.

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