The Hausdorff dimension of elliptic and elliptic-caloric measure in

Author:
Caroline Sweezy

Journal:
Proc. Amer. Math. Soc. **121** (1994), 787-793

MSC:
Primary 35J25; Secondary 30C85, 31A15, 35K20

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186138-X

MathSciNet review:
1186138

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Abstract: The existence of an *L*-caloric measure with parabolic Hausdorff dimension in is demonstrated. The method is to use a specially constructed quasi-disk *Q* whose boundary has Hausdorff . There is an elliptic measure supported on the entire boundary of *Q*. Then the *L*-caloric measure on is compared with the corresponding elliptic measure. The same method gives the existence of an elliptic measure in whose support has Hausdorff for , and an *L*-caloric measure in supported on a set of parabolic Hausdorff dimension .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1186138-X

Keywords:
*L*-caloric measure,
parabolic Hausdorff dimension,
NTA domains

Article copyright:
© Copyright 1994
American Mathematical Society