Intrinsic ultracontractivity of Dirichlet Laplacians in non-smooth domains |
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Authors: | Fabio Cipriani |
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Institution: | (1) SISSA-ISAS Trieste, Italy;(2) Ruhr-Universität Bochum, Germany |
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Abstract: | We give a general criterion for the intrinsic ultracontractivity of Dirichlet Laplacians –
D
on domainsD ofR
d d 3, based on the Lieb's formula. It applies to various classes of domains (e.g. John, Hölder andL
p-averaging domains) and gives new conditions for intrinsic ultracontractivity in terms of the Minkowski dimension of the boundary D. In particular, isotropic self-similar fractals and domains satisfying a c-covering condition are considered. |
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Keywords: | 47F05 35J10 35K05 35P99 |
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