The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Hidemitsu Wadade - One of the best experts on this subject based on the ideXlab platform.
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Brézis-Gallouët-Wainger inequality with a double Logarithmic Term on a bounded domain and its sharp constants
Mathematical Inequalities & Applications, 2011Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:The Brezis-Gallouet-Wainger inequality gives an estimate of the L∞ -norm by the critical Sobolev norm with the aid of the Logarithmic dependency of a higher order Sobolev norm. We investigate the Brezis-Gallouet-Wainger inequality on a bounded domain with the first order critical Sobolev space, and give the best constant in the inequality in some special cases. Furthermore, since the inequality does not hold with the sharp constant, we add a double Logarithmic Term and give the sharp constant for its coefficient. A part of our results is mainly based on an investigation of the inequality with the higher-order Sobolev norm replaced by the Holder seminorm. Mathematics subject classification (2010): 46E35.
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brezis gallouet wainger type inequality with a double Logarithmic Term in the holder space its sharp constants and extremal functions
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:We investigate the sharp constants in a Brezis-Gallouet-Wainger type inequality with a double Logarithmic Term in the Holder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the 2-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ‚ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 2000 Mathematics Subject Classification. Primary 46E35; Secondary 35J85.
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Brézis–Gallouët–Wainger type inequality with a double Logarithmic Term in the Hölder space: Its sharp constants and extremal functions
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:We investigate the sharp constants in a Brezis-Gallouet-Wainger type inequality with a double Logarithmic Term in the Holder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the 2-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ‚ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 2000 Mathematics Subject Classification. Primary 46E35; Secondary 35J85.
Erio Tosatti - One of the best experts on this subject based on the ideXlab platform.
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a fingerprint of surface tension anisotropy in the free energy cost of nucleation
Journal of Chemical Physics, 2013Co-Authors: Santi Prestipino, Alessandro Laio, Erio TosattiAbstract:We focus on the Gibbs free energy ΔG for nucleating a droplet of the stable phase (e.g., solid) inside the metastable parent phase (e.g., liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of ΔG on the droplet volume V, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic Logarithmic Term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy ΔG(V) once more develops a Term Logarithmic on V, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the Logarithmic Term in the droplet free energy, as deTermined from the optimization of its near-coexistence profile.
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A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation
The Journal of chemical physics, 2013Co-Authors: Santi Prestipino, Alessandro Laio, Erio TosattiAbstract:We focus on the Gibbs free energy $\Delta G$ for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of $\Delta G$ on the droplet volume $V$, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic Logarithmic Term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy $\Delta G(V)$ once more develops a Term Logarithmic on $V$, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the Logarithmic Term in the droplet free energy, as deTermined from the optimization of its near-coexistence profile.
Kei Morii - One of the best experts on this subject based on the ideXlab platform.
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Brézis-Gallouët-Wainger inequality with a double Logarithmic Term on a bounded domain and its sharp constants
Mathematical Inequalities & Applications, 2011Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:The Brezis-Gallouet-Wainger inequality gives an estimate of the L∞ -norm by the critical Sobolev norm with the aid of the Logarithmic dependency of a higher order Sobolev norm. We investigate the Brezis-Gallouet-Wainger inequality on a bounded domain with the first order critical Sobolev space, and give the best constant in the inequality in some special cases. Furthermore, since the inequality does not hold with the sharp constant, we add a double Logarithmic Term and give the sharp constant for its coefficient. A part of our results is mainly based on an investigation of the inequality with the higher-order Sobolev norm replaced by the Holder seminorm. Mathematics subject classification (2010): 46E35.
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brezis gallouet wainger type inequality with a double Logarithmic Term in the holder space its sharp constants and extremal functions
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:We investigate the sharp constants in a Brezis-Gallouet-Wainger type inequality with a double Logarithmic Term in the Holder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the 2-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ‚ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 2000 Mathematics Subject Classification. Primary 46E35; Secondary 35J85.
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Brézis–Gallouët–Wainger type inequality with a double Logarithmic Term in the Hölder space: Its sharp constants and extremal functions
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Kei Morii, Tokushi Sato, Hidemitsu WadadeAbstract:We investigate the sharp constants in a Brezis-Gallouet-Wainger type inequality with a double Logarithmic Term in the Holder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the 2-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ‚ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 2000 Mathematics Subject Classification. Primary 46E35; Secondary 35J85.
Santi Prestipino - One of the best experts on this subject based on the ideXlab platform.
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a fingerprint of surface tension anisotropy in the free energy cost of nucleation
Journal of Chemical Physics, 2013Co-Authors: Santi Prestipino, Alessandro Laio, Erio TosattiAbstract:We focus on the Gibbs free energy ΔG for nucleating a droplet of the stable phase (e.g., solid) inside the metastable parent phase (e.g., liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of ΔG on the droplet volume V, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic Logarithmic Term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy ΔG(V) once more develops a Term Logarithmic on V, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the Logarithmic Term in the droplet free energy, as deTermined from the optimization of its near-coexistence profile.
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A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation
The Journal of chemical physics, 2013Co-Authors: Santi Prestipino, Alessandro Laio, Erio TosattiAbstract:We focus on the Gibbs free energy $\Delta G$ for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of $\Delta G$ on the droplet volume $V$, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic Logarithmic Term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy $\Delta G(V)$ once more develops a Term Logarithmic on $V$, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the Logarithmic Term in the droplet free energy, as deTermined from the optimization of its near-coexistence profile.
Marcos Marino - One of the best experts on this subject based on the ideXlab platform.
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a one loop test of quantum supergravity
Classical and Quantum Gravity, 2014Co-Authors: Sayantani Bhattacharyya, Alba Grassi, Marcos MarinoAbstract:The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading Logarithmic Term. Inspired by the success of one-loop quantum gravity for computing the Logarithmic corrections to black hole entropy, we try to reproduce this universal Term by a one-loop calculation in Euclidean 11-dimensional supergravity on AdS4 × X7. We find perfect agreement between the results of ABJM theory and the 11-dimensional supergravity.
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a one loop test of quantum supergravity
arXiv: High Energy Physics - Theory, 2012Co-Authors: Sayantani Bhattacharyya, Alba Grassi, Marcos MarinoAbstract:The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading Logarithmic Term. Inspired by the success of one-loop quantum gravity for computing the Logarithmic corrections to black hole entropy, we try to reproduce this universal Term by a one-loop calculation in Euclidean eleven-dimensional supergravity on AdS_4 \times X_7. We find perfect agreement between the results of ABJM theory and the eleven dimensional supergravity.
