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Menita Carozza, Antonia Passarelli di Napoli  LAHO MA= IKJEI B = ?=II B EA=H AEFJE? IOIJAI

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Menita Carozza, Antonia Passarelli di Napoli

On very weak solutions of a class of nonlinear elliptic systems

Comment.Math.Univ.Carolinae 41,3 (2000) 493-508.

Abstract: In this paper we prove a regularity result for very weak solutions of equations of the type −divA(x, u, Du) = B(x, u, Du), where A, B grow in the gradient liketp−1andB(x, u, Du) is not in divergence form. Namely we prove that a very weak solution u ∈ W1,r of our equation belongs to W1,p. We also prove global higher integrability for a very weak solution for the Dirichlet problem

{ −divA(x, u, Du) =B(x, u, Du) in Ω, u−uo∈W1,r(Ω,Rm).

Keywords: nonlinear elliptic systems, maximal operator theory

AMS Subject Classification: Primary 35J50, 35J55, 35J99; Secondary 46E30

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