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

2021/08/31 by Mikyoung Lee, Lee, Mikyoung, Jihoon Ok +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.13779

openalex publication_date 2021/08/31 · openalex created_date 2021/09/13 · openalex updated_date 2026/08/04

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].

Citations

• On the existence of certain singular integrals
• Global Sobolev regularity for general elliptic equations of p-Laplacian type
• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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