Regularity results for weak solutions of elliptic PDEs below the natural exponent

We prove regularity estimates for the weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give L p estimates for the second derivative for p < 2 . Our work generalizes results due to Miranda (Ann Mat Pura Appl 63(4):353–386, 1963 ).

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2016-06, Vol.195 (3), p.725-740
Main Authors: Cruz-Uribe, David, Moen, Kabe, Rodney, Scott
Format: Article
Language:English
Subjects:
Dirichlet problem
Divergence
Elliptic differential equations
Mathematics
Mathematics and Statistics
Partial differential equations
Regularity
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Description
Summary:We prove regularity estimates for the weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give L p estimates for the second derivative for p < 2 . Our work generalizes results due to Miranda (Ann Mat Pura Appl 63(4):353–386, 1963 ).
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-015-0486-y