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Boundary regularity for certain quasilinear elliptic systems of divergence structure. (English) Zbl 0777.35016
Summary: Consider the Dirichlet problem for a quasilinear elliptic system of the form \[ -D_ j\bigl(a^{ij}(x,u,Du)D_ i u^ k\bigr)=-D_ i f^ i_ k+g^ k, \] and suppose that the structural condition \[ -D_ j\bigl(a^{ij}(x,u,Du)\bigr)=h^ i\in L^ \infty \] is satisfied. Then \(\varepsilon\)-regularity is proven for \(Du\), i.e., under a certain smallness condition any Lipschitz solution has a Hölder continuous gradient in \(\overline\Omega\).
MSC:
35B65 Smoothness and regularity of solutions to PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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