$L^q$-regularity for nonlinear elliptic equations with Schrödinger-type lower order terms

Abstract

We consider nonlinear elliptic equations of the $p$-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse Hölder type condition. Then we obtain interior and boundary $L^q$ estimates for the gradient of weak solutions and the lower order terms, independently, under sharp regularity conditions on the coefficients and the boundaries. In particular, the proof in this paper does not employ Fefferman-Phong type inequalities which are essential tools in the linear cases in [3,47].

22 pages

References in corpus (2)

• Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials
• Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation