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- Title
A Weak Reverse Hölder Inequality for Caloric Measure.
- Authors
Genschaw, Alyssa; Hofmann, Steve
- Abstract
Following a result of Bennewitz–Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Hölder inequality on an open set Ω ⊂ R n + 1 , assuming as a background hypothesis only that the essential boundary of Ω satisfies an appropriate parabolic version of Ahlfors–David regularity (which entails some backwards in time thickness). We also show that the weak reverse Hölder estimate is equivalent to solvability of the initial Dirichlet problem with "lateral" data in L p , for some p < ∞ , in this setting.
- Publication
Journal of Geometric Analysis, 2020, Vol 30, Issue 2, p1530
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-019-00212-4