Boundary regularity for solutions of degenerate elliptic equations. (English) Zbl 0675.35042

The author studies degenerate elliptic equations of the type \(div A(x,u,\nabla u)=B(x,u,\nabla u)\) with \(| p|^{-m}(\partial A_ i/\partial p_ j)(x,u,p)\) uniformly positive definite and bounded for some \(m>-1\). Under standard assumptions interior \(C_{1,\alpha}\)- estimates for bounded solutions have been proved by E. DiBenedetto [Nonlinear Anal., Theory Methods Appl. 7, 827-850 (1983; Zbl 0539.35027)] and P. Tolksdorf [J. Differ. Equations 51, 126-150 (1984; Zbl 0488.35017)]. The author shows the corresponding global regularity-results for both the Dirichlet - and the conormal boundary value problem.
Reviewer: M.Wiegner


35J70 Degenerate elliptic equations
35J67 Boundary values of solutions to elliptic equations and elliptic systems
35B65 Smoothness and regularity of solutions to PDEs
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