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- W4289920906 abstract "We investigate the equation $$(-Delta_{mathbb H^n})^{gamma} w=f(w)quad in mathbb H^{n},$$ where $(-Delta_{mathbb H^n})^gamma$ corresponds to the fractional Laplacian on hyperbolic space for $gamma in (0,1)$ and $f$ is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to $pm 1$ at any point of the two hemispheres $S_pm subset partial_infty mathbb H^n$ and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane $Pi.$ We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when $gamma$ is close to one." @default.
- W4289920906 created "2022-08-06" @default.
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- W4289920906 date "2012-12-31" @default.
- W4289920906 modified "2023-10-16" @default.
- W4289920906 title "Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties" @default.
- W4289920906 doi "https://doi.org/10.48550/arxiv.1212.6830" @default.
- W4289920906 hasPublicationYear "2012" @default.
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