Schrödinger operators involving singular potentials and measure data

Ponce, Augusto;Wilmet, Nicolas
(2017) Journal of Differential Equations — Vol. 263, p. 3581-3610 (2017)

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We study the existence of solutions of the Dirichlet problem for the Schrödinger operator with measure data. We characterize the finite measures for which such a problem has a solution for every nonnegative potential in Lebesgue spaces. The full answer can be expressed in terms of a capacity. We then investigate the existence of a solution of the problem above when the potential belongs to the real Hardy space.
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Ponce, A., & Wilmet, N. (2017). Schrödinger operators involving singular potentials and measure data. Journal of Differential Equations, 263, 3581-3610. https://doi.org/10.1016/j.jde.2017.04.039 (Original work published 2017)