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Regularity of solutions for an integral system of Wolff type. (English) Zbl 1209.45006

The authors consider systems of fully nonlinear integral equations involving Wolff potentials:

u(x)=W β,γ (v q )(x),x n ,v(x)=W β,γ (u p )(x),x n ;


W β,γ (f)(x)= 0 B t (x) f(y)dy t n-βγ 1 γ-1 dt t·

Under some conditions they prove that (1) u,vL ( n ), (2) u,v are Lipschitz continuous.

45G15Systems of nonlinear integral equations
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