Unique solvability for a Schrödinger equation with Robin boundary condition on Lipschitz domains
Volume 136 / 2026
Annales Polonici Mathematici 136 (2026), 275-297
MSC: Primary 42B20; Secondary 35J10
DOI: 10.4064/ap250227-25-9
Published online: 12 May 2026
Abstract
Let $1 \lt p \le 2$. Using the layer potential method, we establish the unique solvability in $L^p$-spaces of the Schrödinger equation $-\varDelta u + \mathbb V u = 0$ on a Lipschitz domain subject to a Robin boundary condition. The potential $\mathbb V$ belongs to the reverse Hölder class. The case of $C^1$-domains is also discussed.
