Necessary and Sufficient Conditions for the Solvability of the Neumann and the Regularity Problems in Lp of Some Schrodinger Equations on Lipschitz Domains

作者：Yang, Sibei^*

来源：Potential Analysis, 2018, 49(4): 527-554.

DOI：10.1007/s11118-017-9666-2

• Schrodinger equation
• Neumann problem
• Regularity problem
• Weak reverse Holder inequality
• Lipschitz domain

Let n = 3 and >= be a bounded Lipschitz domain in Rn. Assume that the nonnegative potential V belongs to the reverse H older class RHn( Rn) and p. ( 2,8). In this article, two necessary and sufficient conditions for the unique solvability of the Neumann and the Regularity problems of the Schr odinger equation - >= u + Vu = 0 in >= with boundary data in Lp, in terms of a weak reverse H older inequality with exponent p and the unique solvability of the Neumann and the Regularity problems with boundary data in some weighted L2 space, are established. As applications, for any p. ( 1,8), the unique solvability of the Regularity problem for the Schr odinger equation - >= u + Vu = 0 in the bounded ( semi-) convex domain >= with boundary data in Lp is obtained.

• 出版日期2018-11
• 单位兰州大学