Challal, Samia2021-10-162021-10-162021Regularity of the Free Boundary in $div(a(x) \nabla u(x,y) )= -(h(x)\gamma(u))_x$ with $h^\prime (x)<0$.. Int. J. Math. And App., 9(4)(2021), 1-11. http://ijmaa.in/v9n4/1.htmlhttp://hdl.handle.net/10315/38566http://ijmaa.in/v9n4/1.htmlA free boundary problem of type div(a(x) grad(u) )= -(h(x)gamma(u))_x with h'(x) < 0 is considered. A regularity of the free boundary as a curve y=Phi(x) is established using a local monotony b u_x-u_y <0 close to free boundary points.enVariational methodsFree boundary problemsLinear elliptic equationsPreprint