Results 21 to 30 of about 24,283 (189)
A Two Well Liouville Theorem [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2005 Summary: We analyse the structure of approximate solutions to the compatible two-well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two-well analogue of the Liouville theorem of \textit{G. Friesecke}, \textit{R. D. James} and \textit{S. Müller}
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Higher-dimensional solutions for a nonuniformly elliptic equation
, 2013 We prove $m$-dimensional symmetry results, that we call $m$-Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\label{mainequ} - div(\gamma(\mathbf x') \nabla u(\mathbf x)) =\lambda ...
Fazly, Mostafa
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The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph
Mathematics, 2022 We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator.
Xian-Biao Wei +2 more
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${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${\mathbb{R}^n}$
, 2014 We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $\mathbb{R}^n$.
Kogoj, Alessia E., Lanconelli, Ermanno
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Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups
, 2015 We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space.
Bonfiglioli, Andrea, Kogoj, Alessia E.
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Liouville Theorem for Dunkl Polyharmonic Functions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 Assume that $f$ is Dunkl polyharmonic in $\mathbb{R}^n$ (i.e. $(\Delta_h)^p f=0$ for some integer $p$, where $\Delta_h$ is the Dunkl Laplacian associated to a root system $R$ and to a multiplicity function $\kappa$, defined on $R$ and invariant with respect to the finite Coxeter group).
Ren, G., Liu, L.
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Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
, 2013 We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations,
Almeida +39 more
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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On Mochizuki-Trooshin Theorem for Sturm-Liouville Operators
Cumhuriyet Science Journal, 2019 In this paper, theinverse spectral problems of Sturm-Liouville operators are considered. Some newuniqueness theorems and analogies of the Mochizuki-Trooshin Theorem are proved.2010 Mathematics Subject Classification. Primary34A55, 34B24; Secondary 34L05.
İbrahim Adalar
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A proof of Liouville’s theorem [PDF]
Proceedings of the American Mathematical Society, 1961 1. S. Bochner, Group invariance of Cauchy's formula in several variables, Ann. of Math. vol. 45 (1944) pp. 686-707. 2. E. Heinz, Ein v. Neumannscher Satz iuber beschriinkte Operatoren im Hilbertschen Raum, Nachr. Akad. Wiss. Gottingen. Math.-Phys. Kl. Ila. (1952) pp. 5-6. 3. J.
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