L<SUP>q</SUP>-regularity for nonlinear elliptic equations with Schrodinger-type lower order terms

초록

We consider nonlinear elliptic equations of the p-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse Holder-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 [P. Auscher and B. Ben Ali, Maximal inequalities and Riesz transform estimates on L-p spaces for Schrodinger operators with nonnegative potentials, Ann. Inst. Fourier (Grenoble) 57(6) (2007) 1975-2013; Z. Shen, On the Neumann problem for Schrodinger operators in Lipschitz domains, Indiana Univ. Math. J. 43(1) (1994) 143-176].

키워드