Challal, Samia2021-10-172021-10-172021"A barrier function for the regularity of the free boundary in div(a(x) grad(u) )= -(h(x) gamma)_x with h'(x) < 0." Int. J. Math. And App., 9(4)(2021), 35-43. http://ijmaa.in/v9n4/4.htmlhttp://hdl.handle.net/10315/38567http://ijmaa.in/v9n4/4.htmlA barrier function is compared to the solution of a class of two dimensional problems near a free boundary point. A regularity of the free boundary is established.enVariational methodsPositive solutionsLinear elliptic equationsA barrier function for the regularity of the free boundary in div(a(x) grad(u) )= -(h(x) gamma)_x with h'(x) < 0Preprint