Orsina, Luigi
[Sapienza U. di Roma, Dipt. Matematica]
Ponce, Augusto
[UCL]
(eng)
Given any Borel function \(V : \Omega \to [0, +\infty]\) on a smooth bounded domain \(\Omega \subset \mathbb{R}^{N}\), we establish that the strong maximum principle for the Schrödinger operator \(-\Delta + V\) in \(\Omega\) holds in each Sobolev-connected component of \(\Omega \setminus Z\), where \(Z \subset \Omega\) is the set of points which cannot carry a Green's function for \(- \Delta + V\). More generally, we show that the equation \(- \Delta u + V u = \mu\) in \(\Omega\) involving a nonnegative finite Borel measure \(\mu\) has a distributional solution in \(W_{0}^{1, 1}(\Omega)\) if and only if \(\mu(Z) = 0\).
Bibliographic reference |
Orsina, Luigi ; Ponce, Augusto. On the nonexistence of Green's function and failure of the strong maximum principle. In: Journal de mathématiques pures et appliquées, Vol. 134, p. 72–121 (2020) |
Permanent URL |
http://hdl.handle.net/2078.1/216690 |