Sharp Uncertainty Principle inequality for solenoidal fields
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Cites
NIST Handbook of Mathematical Functions
Olver, F. W. J., Lozier, D. W., Boisvert, R. F., et al. (2010) · CERN Document Server (European Organization for Nuclear Research) · Cited by 4,809 · see citing works
�ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Heisenberg, W. (1927) · Zeitschrift f�r Physik · doi:10.1007/bf01397280 · Cited by 4,278 · see citing works
The Theory of Groups and Quantum Mechanics
Weyl, H. (1931) · International Linear Collider · Cited by 2,698 · see citing works
Szegő, G. (1939) · Colloquium Publications - American Mathematical Society/Colloquium Publications · doi:10.1090/coll/023 · Cited by 2,161 · see citing works
The uncertainty principle: A mathematical survey
Folland, G. B., & Sitaram, A. (1997) · Journal of Fourier Analysis and Applications · doi:10.1007/bf02649110 · Cited by 957 · see citing works
First order interpolation inequalities with weights
Caffarelli, L. A., Kohn, R. V., & Nirenberg, L. (1984) · French digital mathematics library (Numdam) · Cited by 937 · see citing works
Hardy, G. H. (1920) · Mathematische Zeitschrift · doi:10.1007/bf01199965 · Cited by 622 · see citing works
Leray, J. (1933) · French digital mathematics library (Numdam) · Cited by 612 · see citing works
BIow-up solutions of some nonlinear elliptic problems
Vázquez, J. L., & Brézis, H. (1997) · Revista Matemática Complutense · doi:10.5209/rev_rema.1997.v10.n2.17459 · Cited by 510 · see citing works
A class of self-sustaining dissipative spherical dynamos
Backus, G. (1958) · Annals of Physics · doi:10.1016/0003-4916(58)90054-x · Cited by 331 · see citing works
Best constants in the Hardy–Rellich inequalities and related improvements
Tertikas, A., & Zographopoulos, N. B. (2006) · Advances in Mathematics · doi:10.1016/j.aim.2006.05.011 · Cited by 131 · see citing works
On the analyticity of Laguerre series
Weniger, E. J. (2008) · University of Regensburg Publication Server (University of Regensburg) · Cited by 37 · see citing works
Über quantentheoretische Kinematik und Mechanik
Heisenberg, W. (1926) · Mathematische Annalen · doi:10.1007/bf01206633 · Cited by 31 · see citing works
On the analyticity of Laguerre series
Weniger, E. J. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/42/425207 · Cited by 27 · see citing works
Seventy Five (Thousand) Unsolved Problems in Analysis and Partial Differential Equations
Maz'ya, V. G. (2018) · Integral Equations and Operator Theory · doi:10.1007/s00020-018-2460-8 · Cited by 25 · see citing works
Sharp second order uncertainty principles
Cazacu, C., Flynn, J., & Lam, N. (2022) · Journal of Functional Analysis · doi:10.1016/j.jfa.2022.109659 · Cited by 21 · see citing works
Sharp Hardy–Leray inequality for axisymmetric divergence-free fields
Costin, O., & Maz'ya, V. G. (2008) · Calculus of Variations and Partial Differential Equations · doi:10.1007/s00526-007-0151-4 · Cited by 20 · see citing works
Three-dimensional sharp Hardy–Leray inequality for solenoidal fields
Hamamoto, N. (2019) · Nonlinear Analysis · doi:10.1016/j.na.2019.111634 · Cited by 13 · see citing works
Self-citationSharp Hardy–Leray and Rellich–Leray inequalities for curl-free vector fields
Hamamoto, N., & Takahashi, F. (2019) · Mathematische Annalen · doi:10.1007/s00208-019-01945-x · Cited by 12 · see citing works
Self-citationSharp Rellich-Leray inequality for axisymmetric divergence-free vector fields
Hamamoto, N. (2019) · Calculus of Variations and Partial Differential Equations · doi:10.1007/s00526-019-1592-2 · Cited by 9 · see citing works
Self-citationSharp Hardy-Leray inequality for curl-free fields with a remainder term
Hamamoto, N., & Takahashi, F. (2020) · Journal of Functional Analysis · doi:10.1016/j.jfa.2020.108790 · Cited by 8 · see citing works
Self-citationSharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl
Hamamoto, N., & Takahashi, F. (2020) · Communications on Pure & Applied Analysis · doi:10.3934/cpaa.2020139 · Cited by 6 · see citing works
Self-citationTHE POLOIDAL TOROIDAL DECOMPOSITION OF DIFFERENTIAL FORMS
Weck, N. (1997) · Analysis · doi:10.1524/anly.1997.17.23.265 · Cited by 4 · see citing works
Sharp Rellich–Leray inequality with any radial power weight for solenoidal fields
Hamamoto, N. (2021) · Calculus of Variations and Partial Differential Equations · doi:10.1007/s00526-021-01956-0 · Cited by 4 · see citing works
Self-citationA simpler expression for Costin–Maz’ya’s constant in the Hardy–Leray inequality with weight
Hamamoto, N. (2021) · Archiv der Mathematik · doi:10.1007/s00013-021-01595-z · Cited by 3 · see citing works
Self-citationDuong, A. T., & Nguyen, V. H. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.01425 · Cited by 2 · see citing works
Best constant of the critical Hardy-Leray inequality for curl-free fields in two dimensions
Hamamoto, N., & Takahashi, F. (2021) · Mathematical Inequalities & Applications · doi:10.7153/mia-2021-24-27 · Cited by 2 · see citing works
Self-citationA curl-free improvement of the Rellich-Hardy inequality with weightPreprint
Hamamoto, N., & Takahashi, F. (2021) · Osaka City University (Osaka City University) · doi:10.48550/arxiv.2101.01878 · Cited by 1 · see citing works
Self-citationSharp second order uncertainty principlesPreprint
Cazacu, C., Flynn, J., & Lam, N. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.12667
Flagged first, then by citations
Research works printed but not linked: 3
- [7][7] N. Hamamoto, Sharp Hardy-Leray inequality for solenoidal fields , OCAMI Preprint Series 2020. -
- [12][12] , Sharp Uncertainty Principle inequality for soleonidal fields , arXiv:2104.02351v3 [math.CA] (2021). - · arXiv
- [20][20] J. Leray, ´ Etude de diverses ´ equations int´ egrales non lin´ eaires et de quelques probl` emes que pose l'hydrodynamique , Journal de Math´ ematiques Pures et Appliqu´ ees 12 (1933), 1-82 (French). -
- Authors
- Hamamoto, N.
- Affiliations
- Osaka Metropolitan University (JP)
- Corresponding author
- Hamamoto, Naoki
- Venue
- Journal de Mathématiques Pures et Appliquées
- Publisher
- Elsevier BV
- Published
- 2023-04
- Volume
- 172
- Pages
- 202-235
- ISSN
- 0021-7824 (ISSN-L)
- OpenAlex
- W3151411576
- Cited by
- 8
- References
- 29
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 2 · 2023: 1 · 2022: 1
- FWCI
- 3.16
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Journal de Mathématiques Pures et Appliquées (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science (19H01800, JP21J00172, JP22K13943)
- Tokyo Metropolitan University
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Inequalities and Applications
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Keywords
- solenoidal vector fields, divergence-free vector fields, sharp constants, extremal functions, poloidal magnetic field, toroidal magnetic field, axisymmetric fields, Sobolev spaces
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