A new partial regularity proof for solutions of nonlinear elliptic systems
The author presents a new indirect proof without a reverse Hölder inequality for the partial regularity of weak solutions of the nonlinear elliptic system \(\text{div} A(x,u,Du) + B(x,u,Du) =0\) under natural polynomial growth conditions on \(B\) and suitable conditions on \(A\). The proof uses the method previously obtained by the author in [Ann. Inst. Henri Poincaré, Anal. Non linéaire 13, 255-282 (1996; Zbl 0863.35022)] for establishing the convergence \(w_n \to w\) in \(W^{1,2}_{\text{loc}}\) of a sequence of blow-up functions \(w_n\in W^{1,2} (D,\mathbb{R}^N)\), \(D\) the unit ball, which are known to converge only weakly.
scientific article; zbMATH DE number 1135230