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

TL;DR

This paper studies the regularity and well-posedness of solutions to obstacle problems for fully nonlinear elliptic equations with oblique boundary conditions, establishing existence, uniqueness, and $W^{2,p}$-estimates through approximation and limiting techniques.

Contribution

It introduces a method to obtain $W^{2,p}$-regularity for obstacle problems with oblique boundary conditions by approximating non-obstacle problems and applying a limiting process.

Findings

Established existence and uniqueness of solutions.

Proved $W^{2,p}$-regularity results.

Developed an approximation approach for obstacle problems.

Abstract

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