The interior BMO-regularity for a weak solution of nonlinear second order elliptic systems. (English) Zbl 1055.35042

In this paper the author studies the \(BMO\) regularity for the solution of the following nonlinear elliptic system \[ - D_\alpha\left(A_i^\alpha(Du)\right) = 0, \qquad i=1,\dots,N, \;Ns>1 \] in a bounded domain \(\Omega \subset \mathbb R^n, \;n>2\). Regarding the coefficients of the systems some suitable conditions on the continuity and the differentiability are assumed to hold. The main result of the paper is that the gradient of any solution belongs to the class \(BMO\).


35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J60 Nonlinear elliptic equations
49N60 Regularity of solutions in optimal control
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