Details
| Original language | English |
|---|---|
| Pages (from-to) | 2901-2912 |
| Number of pages | 12 |
| Journal | Journal of Dynamics and Differential Equations |
| Volume | 34 |
| Issue number | 4 |
| Early online date | 16 Mar 2020 |
| Publication status | Published - Dec 2022 |
| Externally published | Yes |
Abstract
We improve the Gagliardo–Nirenberg inequality ‖φ‖Lq(Rn)≤C‖∇φ‖Lr(Rn)L-(1q-n-22n)(‖∇φ‖Lr(Rn)),r= 2 , 0<q<2n(n-2)+, L generalizing L(s)=ln-12s for 0 < s< 1 , from Fila and Winkler (Adv Math 357, 2019. https://doi.org/10.1016/j.aim.2019.106823) for rapidly decaying functions (φ∈ W1 , 2(Rn) \ { 0 } with finite K=∫RnL(|φ|)) by specifying the dependence of C on K and by allowing arbitrary r≥ 1.
Keywords
- Gagliardo–Nirenberg inequality, Interpolation in Lebesgue spaces, Rapidly decaying functions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of Dynamics and Differential Equations, Vol. 34, No. 4, 12.2022, p. 2901-2912.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Gagliardo–Nirenberg Type Inequality for Rapidly Decaying Functions
AU - Fila, Marek
AU - Lankeit, Johannes
N1 - Funding Information: The first author was supported in part by the Slovak Research and Development Agency under the contract No. APVV-18-0308 and by the VEGA grant 1/0347/18. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/12
Y1 - 2022/12
N2 - We improve the Gagliardo–Nirenberg inequality ‖φ‖Lq(Rn)≤C‖∇φ‖Lr(Rn)L-(1q-n-22n)(‖∇φ‖Lr(Rn)),r= 2 , 01 , 2(Rn) \ { 0 } with finite K=∫RnL(|φ|)) by specifying the dependence of C on K and by allowing arbitrary r≥ 1.
AB - We improve the Gagliardo–Nirenberg inequality ‖φ‖Lq(Rn)≤C‖∇φ‖Lr(Rn)L-(1q-n-22n)(‖∇φ‖Lr(Rn)),r= 2 , 01 , 2(Rn) \ { 0 } with finite K=∫RnL(|φ|)) by specifying the dependence of C on K and by allowing arbitrary r≥ 1.
KW - Gagliardo–Nirenberg inequality
KW - Interpolation in Lebesgue spaces
KW - Rapidly decaying functions
UR - http://www.scopus.com/inward/record.url?scp=85082778377&partnerID=8YFLogxK
U2 - 10.1007/s10884-020-09839-2
DO - 10.1007/s10884-020-09839-2
M3 - Article
AN - SCOPUS:85082778377
VL - 34
SP - 2901
EP - 2912
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
IS - 4
ER -