Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary
We study the semiclassical limit to a singularly perturbed nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions, on a Riemannian manifold 𝔐{\mathfrak{M}} with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which con...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-07-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2017-0039 |
| Summary: | We study the semiclassical limit to a singularly perturbed
nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions,
on a Riemannian manifold 𝔐{\mathfrak{M}} with boundary. We exhibit examples of
manifolds, of arbitrary dimension, on which these systems have a solution
which concentrates at a closed submanifold of the boundary of 𝔐{\mathfrak{M}},
forming a positive layer, as the singular perturbation parameter goes to zero.
Our results allow supercritical nonlinearities and apply, in particular, to
bounded domains in ℝN{\mathbb{R}^{N}}. Similar results are obtained for the more
classical electrostatic Klein–Gordon–Maxwell system with appropriate boundary conditions. |
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| ISSN: | 2191-9496 2191-950X |