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On odd Laplace operators
 Geometry, Topology and Mathematical Physics
, 2004
"... We consider odd Laplace operators acting on densities of various weights on an odd Poisson ( = Schouten) manifold M. We prove that the case of densities of weight 1/2 (halfdensities) is distinguished by the existence of a unique odd Laplace operator depending only on a point of an “orbit space ” of ..."
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Cited by 24 (9 self)
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We consider odd Laplace operators acting on densities of various weights on an odd Poisson ( = Schouten) manifold M. We prove that the case of densities of weight 1/2 (halfdensities) is distinguished by the existence of a unique odd Laplace operator depending only on a point of an “orbit space
Infinitesimal aspects of the Laplace operator
, 2000
"... In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second order differential operators. The new neighbourhood has the ..."
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Cited by 1 (0 self)
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In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second order differential operators. The new neighbourhood has
Discrete Laplace operators: No free lunch
, 2007
"... Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set ..."
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Cited by 59 (1 self)
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Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set
On the Zaremba Problem for the pLaplace Operator
"... Abstract. We prove the unique solvability of a mixed boundary value problem for the pLaplace operator by means of variational methods. Using the obtained results, we construct an iterative procedure for solving the Cauchy problem for the pLaplace operator. 1. ..."
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Abstract. We prove the unique solvability of a mixed boundary value problem for the pLaplace operator by means of variational methods. Using the obtained results, we construct an iterative procedure for solving the Cauchy problem for the pLaplace operator. 1.
IMAGINARY POWERS OF LAPLACE OPERATORS
"... Abstract. We show that if L is a secondorder uniformly elliptic operator in divergence form on R d, then C1(1 + α) d/2 ≤ ‖Liα‖L1→L1,∞ ≤ C2(1 + α) d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property. 1. Introduction. Assume that aij ∈ ..."
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Cited by 20 (4 self)
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Abstract. We show that if L is a secondorder uniformly elliptic operator in divergence form on R d, then C1(1 + α) d/2 ≤ ‖Liα‖L1→L1,∞ ≤ C2(1 + α) d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property. 1. Introduction. Assume that aij
Discrete Laplace Operator on Meshed Surfaces
"... In recent years a considerable amount of work in graphics and geometric optimization used tools based on the LaplaceBeltrami operator on a surface. The applications of the Laplacian include mesh editing, surface smoothing, and shape interpolations among others. However, it has been shown [12, 23, 2 ..."
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Cited by 44 (11 self)
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In recent years a considerable amount of work in graphics and geometric optimization used tools based on the LaplaceBeltrami operator on a surface. The applications of the Laplacian include mesh editing, surface smoothing, and shape interpolations among others. However, it has been shown [12, 23
Some special aspects related to the 1Laplace operator
, 2008
"... Some special aspects related to the 1Laplace operator ..."
On odd Laplace operators. II
, 2002
"... We analyze geometry of the second order differential operators, having in mind applications to Batalin–Vilkovisky formalism in quantum field theory. As we show here, an exhaustive picture can be obtained by considering differential operators acting on densities of all weights simultaneously. The alg ..."
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Cited by 5 (1 self)
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We analyze geometry of the second order differential operators, having in mind applications to Batalin–Vilkovisky formalism in quantum field theory. As we show here, an exhaustive picture can be obtained by considering differential operators acting on densities of all weights simultaneously
Measure theoretic Laplace operators on fractals
"... of the euclidean \Delta \Gamma1 on the corresponding Besov spaces. (Since 1996: Triebel a.o.) Remarks. 1. In (1)(3) the construction steps of the selfsimilar fractals play an essential role in the approximation schemes. The Laplacian is here always given as limit operator. 2. Results of Sabo ..."
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Cited by 1 (1 self)
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of Sabot and Metz imply that the approaches (1) and (3) are equivalent for nested fractals. 3. Denker ans Sato have obtained the equivalence of (2) and (3) for the Sierpinski gasket. 4. Comparison of the spectral asymptotics of the Laplace operator in (3) and (4) shows that (4) is different from the other
Results 1  10
of
90,249