Heat kernels on metric measure spaces and an application to semilinear elliptic equations
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AbstractWe consider a metric measure space (M, d, mu) and a heat kernel p(t) (x, y) on M satisfying certain upper and lower estimates, which depend on two parameters alpha and beta. We show that under additional mild assumptions, these parameters are determined by the intrinsic properties of the space (M, d, mu). Namely, alpha is the Hausdorff dimension of this space, whereas beta, called the walk dimension, is determined via the properties of the family of Besov spaces W-sigma,W-2 on M. Moreover, the parameters alpha and beta are related by the inequalities 2 less than or equal to beta less than or equal to alpha + 1.
All Author(s) ListGrigor'yan A, Hu JX, Lau KS
Journal nameTransactions of the American Mathematical Society
Volume Number355
Issue Number5
Pages2065 - 2095
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-22-10 at 00:15