Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping
Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we s...
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| Autor*in: |
Christianson, Hans [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 324(2013), 3 vom: 17. Okt., Seite 657-693 |
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| Übergeordnetes Werk: |
volume:324 ; year:2013 ; number:3 ; day:17 ; month:10 ; pages:657-693 |
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| DOI / URN: |
10.1007/s00220-013-1805-z |
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| 520 | |a Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. | ||
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10.1007/s00220-013-1805-z doi (DE-627)OLC2038905460 (DE-He213)s00220-013-1805-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Christianson, Hans verfasserin aut Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. Wave Packet Phase Function Strichartz Estimate Dispersion Estimate Local Smoothing Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 324(2013), 3 vom: 17. Okt., Seite 657-693 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:324 year:2013 number:3 day:17 month:10 pages:657-693 https://doi.org/10.1007/s00220-013-1805-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 324 2013 3 17 10 657-693 |
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10.1007/s00220-013-1805-z doi (DE-627)OLC2038905460 (DE-He213)s00220-013-1805-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Christianson, Hans verfasserin aut Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. Wave Packet Phase Function Strichartz Estimate Dispersion Estimate Local Smoothing Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 324(2013), 3 vom: 17. Okt., Seite 657-693 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:324 year:2013 number:3 day:17 month:10 pages:657-693 https://doi.org/10.1007/s00220-013-1805-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 324 2013 3 17 10 657-693 |
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10.1007/s00220-013-1805-z doi (DE-627)OLC2038905460 (DE-He213)s00220-013-1805-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Christianson, Hans verfasserin aut Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. Wave Packet Phase Function Strichartz Estimate Dispersion Estimate Local Smoothing Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 324(2013), 3 vom: 17. Okt., Seite 657-693 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:324 year:2013 number:3 day:17 month:10 pages:657-693 https://doi.org/10.1007/s00220-013-1805-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 324 2013 3 17 10 657-693 |
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10.1007/s00220-013-1805-z doi (DE-627)OLC2038905460 (DE-He213)s00220-013-1805-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Christianson, Hans verfasserin aut Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. Wave Packet Phase Function Strichartz Estimate Dispersion Estimate Local Smoothing Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 324(2013), 3 vom: 17. Okt., Seite 657-693 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:324 year:2013 number:3 day:17 month:10 pages:657-693 https://doi.org/10.1007/s00220-013-1805-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 324 2013 3 17 10 657-693 |
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10.1007/s00220-013-1805-z doi (DE-627)OLC2038905460 (DE-He213)s00220-013-1805-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Christianson, Hans verfasserin aut Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. Wave Packet Phase Function Strichartz Estimate Dispersion Estimate Local Smoothing Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 324(2013), 3 vom: 17. Okt., Seite 657-693 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:324 year:2013 number:3 day:17 month:10 pages:657-693 https://doi.org/10.1007/s00220-013-1805-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 324 2013 3 17 10 657-693 |
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Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping |
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Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. © Springer-Verlag Berlin Heidelberg 2013 |
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Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. © Springer-Verlag Berlin Heidelberg 2013 |
| abstract_unstemmed |
Abstract We consider an n-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for a time scale polynomially beyond Ehrenfest time, we show that solutions to the linear Schrödinger equation with initial conditions localized on a spherical harmonic satisfy Strichartz estimates with a loss depending only on the dimension n and independent of the degeneracy. The Strichartz estimates are sharp up to an arbitrary β > 0 loss. This is in contrast to Christianson and Wunsch (Amer J Math, 2013), where it is shown that solutions satisfy a sharp local smoothing estimate with loss depending only on the degeneracy of the trapped set, independent of the dimension. © Springer-Verlag Berlin Heidelberg 2013 |
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Near Sharp Strichartz Estimates with Loss in the Presence of Degenerate Hyperbolic Trapping |
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