Conductive Homogeneity of Compact Metric Spaces and Construction of p-Energy
Seiten
In the ordinary theory of Sobolev spaces on domains of ℝ^n, the p-energy is defined
as the integral of |∇f |p. In this paper, we try to construct a p-energy on compact metric spaces as a scaling
limit of discrete p-energies on a series of graphs approximating the original space. In conclusion, we propose
a notion called conductive homogeneity under which one can construct a reasonable p-energy if p is
greater than the Ahlfors regular conformal dimension of the space. In particular, if p = 2, then we construct
a local regular Dirichlet form and show that the heat kernel associated with the Dirichlet form satisfies upper
and lower sub-Gaussian type heat kernel estimates. As examples of conductively homogeneous spaces,
we present new classes of square-based self-similar sets and rationally ramified Sierpiński crosses, where no
diffusions were constructed before.
as the integral of |∇f |p. In this paper, we try to construct a p-energy on compact metric spaces as a scaling
limit of discrete p-energies on a series of graphs approximating the original space. In conclusion, we propose
a notion called conductive homogeneity under which one can construct a reasonable p-energy if p is
greater than the Ahlfors regular conformal dimension of the space. In particular, if p = 2, then we construct
a local regular Dirichlet form and show that the heat kernel associated with the Dirichlet form satisfies upper
and lower sub-Gaussian type heat kernel estimates. As examples of conductively homogeneous spaces,
we present new classes of square-based self-similar sets and rationally ramified Sierpiński crosses, where no
diffusions were constructed before.
Kyoto University, Japan
| Erscheinungsdatum | 14.07.2023 |
|---|---|
| Reihe/Serie | MEMOIRS OF THE EUROPEAN MATHEMATICAL SOCIETY ; 5 |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | conductive homogeneity • Metric Spaces • p-energy • Self-Similar Sets • Sobolev spaces |
| ISBN-13 | 9783985470563 / 9783985470563 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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