On coercivity and regularity for linear elliptic systems

  • Kewei ZhangEmail author


We introduce a nonlinear method to study a ‘universal’ strong coercivity problem for monotone linear elliptic systems by compositions of finitely many constant coefficient tensors satisfying the Legendre–Hadamard strong ellipticity condition. We give conditions and counterexamples for universal coercivity. In the case of non-coercive systems we give examples to show that the corresponding variational integral may have infinitely many nowhere C 1 minimizers on their supports. For some universally coercive systems we also present examples with affine boundary values which have nowhere C 1 solutions.

Mathematics Subject Classification (2000)

35J47 35J50 35B60 49J45 49J10 49N60 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsSwansea UniversitySwanseaUK

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