The Hardy–Morrey & Hardy–John–Nirenberg inequalities involving distance to the boundary

We strengthen the classical inequality of C.B. Morrey concerning the optimal Hölder continuity of functions in W1,p when p>n, by replacing the Lp-modulus of the gradient with the sharp Hardy difference involving distance to the boundary. When p=n we do the same strengthening in the integral form...

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Bibliographic Details
Published in:Journal of Differential Equations 2016-09, Vol.261 (6), p.3107-3136
Main Authors: Filippas, Stathis, Psaradakis, Georgios
Format: Article
Language:English
Subjects:
Bounded mean oscillation
Hardy–Morrey inequality
Hardy–Sobolev inequality
Weighted Sobolev embedding
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Summary:We strengthen the classical inequality of C.B. Morrey concerning the optimal Hölder continuity of functions in W1,p when p>n, by replacing the Lp-modulus of the gradient with the sharp Hardy difference involving distance to the boundary. When p=n we do the same strengthening in the integral form of a well known inequality due to F. John and L. Nirenberg.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2016.05.021