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...
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De Gruyter
2017-07-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2017-0039 |
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doaj-767a0844ecf24b348b9ccc3b706846512021-09-06T19:39:55ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2017-07-018155958210.1515/anona-2017-0039anona-2017-0039Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundaryClapp Mónica0Ghimenti Marco1Micheletti Anna Maria2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510México City, MexicoDipartimento di Matematica Applicata, Università di Pisa, Via Buonarroti 1/c 56127, Pisa, ItalyDipartimento di Matematica Applicata, Università di Pisa, Via Buonarroti 1/c 56127, Pisa, ItalyWe 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.https://doi.org/10.1515/anona-2017-0039electrostatic klein–gordon–maxwell–proca systemsemiclassical limitboundary layerriemannian manifold with boundarysupercritical nonlinearitylyapunov–schmidt reduction35j60 35j20 35b40 53c80 58j32 81v10 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Clapp Mónica Ghimenti Marco Micheletti Anna Maria |
| spellingShingle |
Clapp Mónica Ghimenti Marco Micheletti Anna Maria Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary Advances in Nonlinear Analysis electrostatic klein–gordon–maxwell–proca system semiclassical limit boundary layer riemannian manifold with boundary supercritical nonlinearity lyapunov–schmidt reduction 35j60 35j20 35b40 53c80 58j32 81v10 |
| author_facet |
Clapp Mónica Ghimenti Marco Micheletti Anna Maria |
| author_sort |
Clapp Mónica |
| title |
Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary |
| title_short |
Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary |
| title_full |
Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary |
| title_fullStr |
Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary |
| title_full_unstemmed |
Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary |
| title_sort |
boundary layers to a singularly perturbed klein–gordon–maxwell–proca system on a compact riemannian manifold with boundary |
| publisher |
De Gruyter |
| series |
Advances in Nonlinear Analysis |
| issn |
2191-9496 2191-950X |
| publishDate |
2017-07-01 |
| description |
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. |
| topic |
electrostatic klein–gordon–maxwell–proca system semiclassical limit boundary layer riemannian manifold with boundary supercritical nonlinearity lyapunov–schmidt reduction 35j60 35j20 35b40 53c80 58j32 81v10 |
| url |
https://doi.org/10.1515/anona-2017-0039 |
| work_keys_str_mv |
AT clappmonica boundarylayerstoasingularlyperturbedkleingordonmaxwellprocasystemonacompactriemannianmanifoldwithboundary AT ghimentimarco boundarylayerstoasingularlyperturbedkleingordonmaxwellprocasystemonacompactriemannianmanifoldwithboundary AT michelettiannamaria boundarylayerstoasingularlyperturbedkleingordonmaxwellprocasystemonacompactriemannianmanifoldwithboundary |
| _version_ |
1717769795523313664 |