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The kernel space of linear operator for a class of Grushin equation
Topological Methods in Nonlinear AnalysisIn this paper, we concern the kernel of linear operator for a class of Grushin equation. First, we study the kernel space of linear operator for a general Grushin equation. Then, we provide an exact expression for the kernel space of linear operator associated with a special Grushin equation.
Yawei Wei, Xiaodong Zhou
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Pullback attractors for non-autonomous parabolic equations involving Grushin operators
Electronic Journal of Differential Equations, 2010 Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain.
Cung The Anh
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Fundamental solutions to the p-Laplace equation in a class of Grushin vector fields
Electronic Journal of Differential Equations, 2011 We find the fundamental solution to the p-Laplace equation in a class of Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in ...
Thomas Bieske
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L^p estimates for the wave equation associated to the Grushin operator
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2014 We prove that the solution of the wave equation as- sociated to the Grushin operator $ G = -Δ+|x|^2 \partial_t^2 $ is bounded on $ L^p(R^{n+1})(1 < p < \infty)$, when $|1/p- 1/2 | < 1/n+2$ .
Jotsaroop, Kaur, Thangavelu, Sundaram
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Lie Group Approach to Grushin Operators
Journal of Lie Theory, 2021 We consider a finite system $\{X_1, X_2, \ldots, X_n\}$ of complete vector fields acting on smooth manifolds $M$ equipped with a smooth positive measure. We assume that the system satisfies Hörmander's condition and generates a finite dimensional Lie algebra of type (R).
Dziubanski, Jacek, Sikora, Adam
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An Optimal Multiplier Theorem for Grushin Operators in the Plane, II
Journal of Fourier Analysis and Applications, 2022 Let \mathcal{L} = -\partial_x^2 - V(x) \partial_y^2 be the Grushin operator on \mathbb{R}^2 with coefficient V \colon ...
Gian Maria Dall’Ara, Alessio Martini
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Turbocharging synaptic transmission
FEBS Letters, Volume 597, Issue 18, Page 2233-2249, September 2023., 2023 State1, a vesicle is captured by the six Upright Munc13s and pSNAREpins are formed by the outer VAMP2. State 2, diacylglycerol binding rearranges Munc13s to lateral closed conformation. State 3, the vesicle proceeds to a readily releasable pool. All pSNAREpins concomitantly exert high pressure for a longer time to ‘turbocharge’ the neurotransmitter ...
James E. Rothman +3 more
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The Chemical Record, Volume 23, Issue 9, September 2023., 2023 In recent years, the rise of both organofluorine chemistry and photochemistry have intersected to bring about a myriad of visible light‐mediated protocols. The development of new reagents and advances in photo‐mediated processes have synergistically provided mild, effective, and reliable fluorine‐related transformations.
Daniel Lin +4 more
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The Chemical Record, Volume 23, Issue 9, September 2023., 2023 The propensity of Ag to undergo 1e− redox events makes Ag an unlikely catalyst in cross‐coupling. However, isolable organo‐AgIII species bearing macrocycles or perfluorinated ligands were recently found active in C−C and C‐heteroatom bond formation. Main advances in aryl‐F and aryl‐CF3 couplings proceeding via AgI/AgIII redox sequences, and comparison ...
Luca Demonti +2 more
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Chemistry – A European Journal, Volume 29, Issue 41, July 20, 2023., 2023 A combination of gas‐phase fragmentation experiments and quantum chemical calculations affords detailed insight into the reactivity of high‐valent trifluoromethylated cuprate complexes. Depending on the nature of the organyl group R, these key intermediates of synthetically valuable trifluoromethylation reactions lose two radicals or undergo concerted ...
Bastian Zimmer +2 more
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