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On very weak solutions of a class of nonlinear elliptic systems. (English) Zbl 1119.35016
The paper is devoted to the study of a very weak solution of the equation \(\text{div}\;A(x,u,Du)=B(x,u,Du)\), where \(A\), \(B\) grow in the gradient like \(t^{p-1}\) and \(B(x,u,Du)\) is not in divergence form. The author prove that a very weak solution \(u\in W^{1,r}\) of this equation belongs to \(W^{1,p}\).

MSC:
35J50 Variational methods for elliptic systems
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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