On coercivity and regularity for linear elliptic systems. (English) Zbl 1208.35044
Author’s abstract: 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.
Reviewer: Stepan Agop Tersian (Rousse)
MSC:
| 35J47 | Second-order elliptic systems |
| 35J50 | Variational methods for elliptic systems |
| 35B60 | Continuation and prolongation of solutions to PDEs |
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