Interior and boundary W^1,q-estimates for quasi-linear elliptic equations of Schrödinger type

2019/12/13 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.1912.06283

openalex publication_date 2019/12/13 · openalex created_date 2020/04/03 · openalex updated_date 2026/07/28

Abstract

We consider nonlinear elliptic equations that are naturally obtained from the elliptic Schrödinger equation -Δu +Vu=0 in the setting of the calculus of variations, and obtain L^q-estimates for the gradient of weak solutions. In particular, we generalize a result of Shen in [Ann. Inst. Fourier 45 (1995), no. 2, 513--546] in the nonlinear setting by using a different approach. This allows us to consider discontinuous coefficients with a small BMO semi-norm and non-smooth boundaries which might not be Lipschitz continuous.

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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