I am looking for a theory to handle an elliptic equation with square root of Laplacian involved. Namely, $$ (-\Delta)^{1/2} v(x) + c(x) v(x) = f(x),$$ with relevant boundary conditions. Here I can assume $c(x) > 0$ if necessary. Any result in 1-D periodic setting would be also helpful because that is what I have in mind for now. Any books or papers to look at? Thank you!
2026-03-25 15:49:55.1774453795
Solvability of a simple nonlocal elliptic equation.
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Maybe have a look at
https://www.uni-due.de/imperia/md/images/mathematik/ruhr_pad/ruhrpad-2020-04.pdf
where existence and uniqueness of so called entropy solutions is shown to an equation involving the fractional Laplacian. From a quick look I would say the equation dealt with in the upper paper is a little more involved, maybe it helps anyways.