We collect some interesting results for equations driven by the fractional relativistic Schrödinger operator (−Δ+m2)s with s∈(0,1) and m>0. More precisely, for the linear theory, we prove Hölder-Schauder-Zygmund regularity results and a Kato's inequality. For the nonlinear theory, we obtain L∞-regularity, exponential decay, a Pohozaev-type identity, and a symmetry result for solutions of certain nonlinear fractional problems.
On the fractional relativistic Schrödinger operator / Ambrosio, V.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 308:(2022), pp. 327-368. [10.1016/j.jde.2021.07.048]
On the fractional relativistic Schrödinger operator
Ambrosio V.
2022-01-01
Abstract
We collect some interesting results for equations driven by the fractional relativistic Schrödinger operator (−Δ+m2)s with s∈(0,1) and m>0. More precisely, for the linear theory, we prove Hölder-Schauder-Zygmund regularity results and a Kato's inequality. For the nonlinear theory, we obtain L∞-regularity, exponential decay, a Pohozaev-type identity, and a symmetry result for solutions of certain nonlinear fractional problems.| File | Dimensione | Formato | |
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