Lp Neumann problem for some Schrödinger equations in (semi-)convex domains

Author:

Yang Sibei1,Yang Dachun2

Affiliation:

1. Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China

2. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

Abstract

Let [Formula: see text], [Formula: see text] be a bounded (semi-)convex domain in [Formula: see text] and the non-negative potential [Formula: see text] belong to the reverse Hölder class [Formula: see text]. Assume that [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the Muckenhoupt weight class on [Formula: see text], the boundary of [Formula: see text]. In this paper, the authors show that, for any [Formula: see text], the Neumann problem for the Schrödinger equation [Formula: see text] in [Formula: see text] with boundary data in (weighted) [Formula: see text] is uniquely solvable. The obtained results in this paper essentially improve the known results which are special cases of the results obtained by Shen [Indiana Univ. Math. J. 43 (1994) 143–176] and Tao and Wang [Canad. J. Math. 56 (2004) 655–672], via extending the range [Formula: see text] of [Formula: see text] into [Formula: see text].

Funder

National Natural Science Foundation of China

Fundamental Research Funds for the Central Universities

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

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