Bounded Minimisers of Double Phase Variational Integrals

Bounded minimisers of the functional w ↦ ∫ ( | D w | p + a ( x ) | D w | q ) d x , where 0 ≦ a ( · ) ∈ C 0 , α and 1 < p < q , are C 1 , β -regular provided the sharp bound q ≦ p + α holds.

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2015-10, Vol.218 (1), p.219-273
Main Authors: Colombo, Maria, Mingione, Giuseppe
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Description
Summary:Bounded minimisers of the functional w ↦ ∫ ( | D w | p + a ( x ) | D w | q ) d x , where 0 ≦ a ( · ) ∈ C 0 , α and 1 < p < q , are C 1 , β -regular provided the sharp bound q ≦ p + α holds.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-015-0859-9