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The existence of regular boundary points for nonlinear elliptic systems. (English) Zbl 1214.35021

Summary: We consider nonlinear elliptic systems of the type \[ -\text{div}\, a(x, u, Du) = 0, \] with Hölder continuous dependence on \((x, u)\), and give conditions guaranteeing that \(\mathcal H ^{n-1}\)- almost every boundary point is a regular point for the gradient of solutions to related Dirichlet problems. We also introduce a new comparison technique, in order to deal with difference quotients.

MSC:

35J57 Boundary value problems for second-order elliptic systems
35J60 Nonlinear elliptic equations
35J67 Boundary values of solutions to elliptic equations and elliptic systems
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