Borderline gradient continuity of minima



The gradient of any local minimiser of functionals of the type \({w \mapsto \int_{\Omega}{f(x, w, Dw)}dx + \int_{\Omega}{w\mu}dx}\), where f has p-growth, p >  1, and \({\Omega \subset \mathbb{R}^{n}}\), is continuous provided that the optimal Lorentz space condition \({\mu \in L(n, 1)}\) is satisfied and \({x \rightarrow f(x, \cdot)}\) is suitably Dini continuous.


Nondifferentiable functionals gradient continuity Lorentz spaces 

Mathematics Subject Classification

Primary 49N60 Secondary 35J20 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden
  2. 2.Institute of MathematicsAalto UniversityAaltoFinland
  3. 3.Dipartimento di Matematica e InformaticaUniversità di ParmaParmaItaly

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