Hölder continuity of normalized solutions of the Schrödinger equation. (English) Zbl 0822.35033
From the authors’ introduction: “We investigate the behavior of local weak solutions of the Schrödinger equation \((- \Delta/2+ V)u=0\) with a potential \(V\geq 0\) on \(\mathbb{R}^ d\), \(d\geq 2\). We aim to give lower bounds for the Hölder exponents of quotients of positive solutions to the Schrödinger equation. Our main result states that the quotients are Hölder continuous of order arbitrarily close to 1 if the solutions of the original equation are continuous”.
Reviewer: M.Chicco (Genova)
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 31B15 | Potentials and capacities, extremal length and related notions in higher dimensions |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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