On $$W^{2,p}$$-estimates for solutions of obstacle problems for fully nonlinear elliptic equations with oblique boundary conditions

Abstract

This paper concerns fully nonlinear elliptic obstacle problems with oblique boundary conditions. We investigate the existence, uniqueness and $$W^{2,p}$$ W 2 , p -regularity results by finding approximate non-obstacle problems with the same oblique boundary condition and then making a suitable limiting process.

W2,-estimates for fully nonlinear elliptic equations with oblique boundary conditions

“…For the oblique boundary condition D. Li and K. Zhang [30] obtained regularity estimates results such as C 1,α on a C 1 domain for the uniformly elliptic case. Further notable regularity results regarding the Neumann and oblique boundary condition are to be found in for uniformly elliptic equation, see [9,8,10,16,17], etc.…”