Non-parametric minimal surfaces with discontinuous and thin obstacles

@article{Giusti1972NonparametricMS,
  title={Non-parametric minimal surfaces with discontinuous and thin obstacles},
  author={Enrico Giusti},
  journal={Archive for Rational Mechanics and Analysis},
  year={1972},
  volume={49},
  pages={41-56}
}
In this paper, we are concerned with the regularity of the solution to the nonparametric Plateau problem with obstacles. Let I2 be an open bounded set in ~ " , whose boundary af t is a C3-surface of non-negative mean curvature, and let A be a closed set contained in the closure of ft, ~. Let q~ (x) be a non-negative continous function in aft , and let ~(x) be a continuous function in ~, such that r in Oft.