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Everywhere regularity for a class of elliptic systems without growth conditions. (English) Zbl 0922.35031

The author proves \(W^{1,\infty}\) regularity of solutions to diagonal elliptic systems which originate from integral functionals with strong growth such as \[ F(v)= \int_\Omega f(Dv)dx \] with \(f(Dv)= \exp(| Dv|^p)\) and \(p\geq 2\). The strong growth of the integrand is used to prove these estimates. Once the solution is known to be in \(W^{1,\infty}\), only local growth properties of \(f\) are needed to prove further regularity. The case of scalar equations was treated by the author in [J. Optimization Theory Appl. 90, No. 1, 161-181 (1996; Zbl 0901.49030)].
Reviewer: B.Kawohl (Köln)

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35J45 Systems of elliptic equations, general (MSC2000)
49N60 Regularity of solutions in optimal control

Citations:

Zbl 0901.49030
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