Local behavior of smooth functions for the energy Laplacian on the Sierpinski gasket
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Robert S. Strichartz
Abstract
We consider the energy Laplacian Δν on the Sierpinski gasket (SG), which is defined by the standard self-similar energy E and the Kusuoka measure, and is different from the standard self-similar Laplacian Δ. We study the local behavior of function u∈domΔνk near a boundary point q0. We define jets of local derivatives at q0 and estimate the decay rate of u near q0 in terms of the vanishing of jet. This can be used to define Taylor approximating polynomials with error estimates. Analogous results are known for the standard Laplacian, but the results here are quite different. We also confirm experimentally the absolute continuity of different energy measures, and give experimental evidence that the density is p-integrable for p < log(15)/log(9).
© by Oldenbourg Wissenschaftsverlag, Canada N2L 3G1, Germany
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- On a modification of Wong´s asymptotic expansion of the Kontorovich–Lebedev transform
- Regularity results for generalized electro-magnetic problems
- Neck pinching for periodic mean curvature flows
- Zur Regularität von drei Integralen im Hilbertraum
- Generalized radon transform on the sphere
- Local behavior of smooth functions for the energy Laplacian on the Sierpinski gasket
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Artikel in diesem Heft
- On a modification of Wong´s asymptotic expansion of the Kontorovich–Lebedev transform
- Regularity results for generalized electro-magnetic problems
- Neck pinching for periodic mean curvature flows
- Zur Regularität von drei Integralen im Hilbertraum
- Generalized radon transform on the sphere
- Local behavior of smooth functions for the energy Laplacian on the Sierpinski gasket
- On the existence of para-orthogonal rational functions on the unit circle
